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This is to certify that the

dissertation entitled

The Application of Capture-Recapture for
Indirect Population Estimation

presented by

Lori Ann Wibert

has been accepted towards fulﬁllment
of the requirements for

Ph.D. degree in Sociology

Mai-W

Major professor

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THE APPLICATION OF CAPTURE-RECAPTURE FOR INDIRECT POPULATION
ESTIMATION

By

Lori Ann Wibert

A DISSERTATION

Submitted to
Michigan State University
In partial fulﬁllment of the requirements
For the degree of

DOCTOR OF PHILOSOPHY
Department of Sociology

1998

ABSTRACT
THE APPLICATION OF CAPTURE-RECAPTURE FOR INDIRECT POPULATION
ESTIMATION
By

Lori Ann Wibert

Sociologists maintain two tenets when it comes to population estimation - - a census or a
sample. Both estimation procedures are limited for counting hidden populations such as
domestic violence. Victims are not represented in random surveys because of sampling
bias while registries from police departments and shelters are incomplete because most
persons never report their crime. This dissertation borrows a methodology from animal
population scientists known as capture-recapture which involves tagging individuals and
matching them between samples to estimate the invisible population. These ﬁndings
suggest violence from intimate partners is more pervasive than indicated from national

studies and that women are battered more than 17 times the rate of men.

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. vi
LIST OF FIGURES .......................................................................................................... vii
CHAPTER 1 -- INTRODUCTION .................................................................................... 1
I. Introduction ............................................................................................................. 1
II. Literature Review .................................................................................................... 2
A. The Maj or Theoretical Perspectives ................................................................... 2

1. The Family Violence Perspectives ...................................................................... 4

2. The Feminist Perspectives .................................................................................. 7

B. Limitations of Theoretical Perspectives .............................................................. 9

1. Female on Male Violence ................................................................................... 9

2. Conflict based ................................................................................................... 10

3. Broad Generalization ........................................................................................ 11

4. Ageism .............................................................................................................. 11

5. Sampling Error .................................................................................................. 12

6. Univariate Explanation ..................................................................................... 12

7. Clinical Fallacy ................................................................................................. 12

III. Methodological Barriers Impede Theoretical Development ................................. 13
IV. Research Methodological Challenges in Sociology .............................................. 14
V. Solution to the Problem ........................................................................................ 15
VI. Research Signiﬁcance ........................................................................................... 15
CHAPTER 2 —- METHODS AND TECHNIQUES .......................................................... 19
I. Research Application ............................................................................................ 19
11. Research Questions ............................................................................................... 19
III. Operational Defmitions ......................................................................................... 22
IV. Capture / Recapture ............................................................................................... 23
V. Capture / Recapture in Wildlife Population Estimation ....................................... 25
VI. Capture / Recapture Applied to Marquette County .............................................. 28
VII. Satisfying the Necessary Assumptions for Capture / Recapture ...................... 30
A. Source Dependency / Independence ................................................................. 32

B. Population Stability ........................................................................................... 34

C. Catchability ....................................................................................................... 35

D. True Cases and Accurate Matching .................................................................. 35
VIII. Validation of Capture / Recapture .................................................................... 36
D(. Relational Databases for Capture/Recapture Analysis ......................................... 38
X. Population of Interest ............................................................................................ 41
A. Marquette County, Michigan ............................................................................ 41

B. The Study .......................................................................................................... 43

XI. Data ....................................................................................................................... 43
XII. Limitations ........................................................................................................ 45
XIII. Summation ........................................................................................................ 45
CHAPTER 3 - SIMULATIONS ...................................................................................... 47

iii

I Introduction ........................................................................................................... 47

II. The Logistics of Capture-Recapture ..................................................................... 48
111. Effects of Database Sensitivity to Model .............................................................. 50
VI. Yes, but does it really work? ................................................................................. 53
A. Empirical Reality .............................................................................................. 54
B. Other Applications ............................................................................................ 54
C. The Precision of the Capture-Recapture technique .......................................... 55
D. Distribution of Capture-Recapture Estimates ................................................... 56
V. Conclusions ........................................................................................................... 57
CHAPTER 4 - CAPTURE-RECAPTURE ...................................................................... 59
1. Subject and Database Descriptions ....................................................................... 59
II. Male-on-Female Intimate Partner Violence .......................................................... 62
III. Necessary Assumptions ........................................................................................ 63
A. Closure .............................................................................................................. 63
B. Perfect matching ............................................................................................... 63
C. Independence .................................................................................................... 65
D. Homogeneity ..................................................................................................... 67
IV. Maximum Likelihood Estimator (MLE) ............................................................... 69
V. Log-linear Modeling to Control for Sample Dependency .................................... 72
VI. Establishing Incidence and Prevalence. ................................................................ 74
VII. Stratifying the Data ........................................................................................... 78
VIII. Calculating Standard Error for Capture-Recapture Models .............................. 81
D(. Point Estimates for Capture-Recapture ................................................................. 82
X. Female-on-Male Violence .................................................................................... 84
XI. Conclusions ........................................................................................................... 86
CHAPTER 5 - COMPARATIVE STUDIES OF INTIMATE PARTNER VIOLENCE 88
I. Introduction ........................................................................................................... 88
11. Survey Studies ...................................................................................................... 88
A. Michigan Violence Against Women Study ...................................................... 88

1. Sample ............................................................................................................... 89

2. Marital Status .................................................................................................... 89

3. Deﬁnition .......................................................................................................... 89

4. Gender ............................................................................................................... 89

5. Rates .................................................................................................................. 90

B. The National Crime Victim’s Survey .................................................................. 9O

1. Sample ............................................................................................................... 9O

2. Marital Status .................................................................................................... 91

3. Deﬁnition .......................................................................................................... 91

4. Gender ............................................................................................................... 91

5. Rates .................................................................................................................. 91

C. The National Family Violence Survey ............................................................. 91

1. Sample ............................................................................................................... 92

2. Marital Status .................................................................................................... 92

3. Deﬁnition .......................................................................................................... 92

4. Gender ............................................................................................................... 92

iv

5. Rates .................................................................................................................. 92

III. Comparative Estimates from Capture-Recapture ................................................. 93
1. Sample ............................................................................................................... 93

2. Marital Status .................................................................................................... 93

3. Deﬁnition .......................................................................................................... 93

4. Gender ............................................................................................................... 93

5. Rates .................................................................................................................. 94

IV. Methodological Limitations and Variances .......................................................... 95
A. Intimate Partner Status ...................................................................................... 95
B. Survey research ................................................................................................. 96
C. Gender symmetry/asymmetry ........................................................................... 97
D. Agency Studies ................................................................................................. 99
E. Pretense of Study .............................................................................................. 99
F. Respondents .................................................................................................... 100
G. Age Parameters ............................................................................................... 100
H. Bounding ......................................................................................................... 100
V. Conclusions ......................................................................................................... 101
CHAPTER 6 — CONCLUSION ...................................................................................... 103
1. Summary ofDissertation.................................................-. .................................. 103
A. Theoretical Lull .............................................................. 103
B. Theoretical Impasse ........................................................................................ 105
C. Methods Suspend Theoretical Development and Testing .............................. 105
D. Capture-Recapture .......................................................................................... l 07
II. Signiﬁcance of Study .......................................................................................... 111
A Paradigm Shift ................................................................................................ 111
B. Tests Existing Theories of Intimate Partner Violence .................................... 111
C. Methods Have Provided Room for Theoretical Development ....................... 112

D Tests Precision and Sensitivity of Capture-Recapture .................................... 114

E Future Applications ......................................................................................... 114

F Limitations ...................................................................................................... 115

1. Cannot Positively Differentiate Violence Types ............................................ 115

2. Measures more severe forms of Violence and Only Physical Violence ......... 116

3. Does not provide individual level data ........................................................... 117

G. Conclusion ...................................................................................................... l 18
REFERENCES ............................................................................................................... 119

LIST OF TABLES

Table 3.1 Hypothetical Samples ....................................................................................... 50
Table 3.2 Probabilities of Being Captured ........................................................................ 53
Table 3.3 Measure of Precision ........................................................................................ 56
Table 4.1 Sections and Intersections of 3 Sources ............................................................ 70
Table 4.2 Interactions According to Model ...................................................................... 74
Table 4.3 Incidence and Prevalence MLE by Model ........................................................ 75
Table 4.4 Two-source Restricted Models for Three Data Sources ................................... 75
Table 4.5 Prevalence Estimations Stratiﬁed by Age ........................................................ 79
Table 4.6 Prevalence Estimates According to Age ........................................................... 79
Table 4.7 Estimated Number of Women by Model .......................................................... 83
Table 5.1 Survey Estimates ............................................................................................... 94

vi

LIST OF FIGURES

Figure 2.1 Two Sample Database Overlap ...................................................................... 28
Figure 2.2 Contingency Table of 2-Source Capture-Recapture ....................................... 31
Figure 2.3 Flap VS. Relational Database ......................................................................... 40
Figure 3.1 Sections of Probability ................................................................................... 52
Figure 3.2 Distribution of Capture-Recapture Estimates ................................................. 57
Figure 4.1 Analytic Sources for Capture-Recapture ........................................................ 59
Figure 4.2 Overlap of Incidence Data Sources ................................................................ 69
Figure 4.3 Overlap of Prevalence Data Sources .............................................................. 70
Figure 4.4 Contingency Table for Three Sources ............................................................ 72

vii

CHAPTER 1 -- INTRODUCTION

1. Introduction

Social scientists have been investigating intimate partner violence for less than 30
years even though it has always permeated family life. Intimate partner violence as a
scholarly focus differed from other topics of social research because concurrent with
academic development, activists and professionals were advocating for victim's rights.
Some researchers developed within the battered women's movement and some studied it
abstractly from the outside. Researchers and advocates originated from different
backgrounds and goals that led to opposing points of view (Geffener, 1987; Jacobson,
1994; Schechter, 1988). There has been dissension not only between activists and
academics but also between disciplines within academia (Yllo, 1997). From the very
beginning, researchers on this social problem were at odds. Fagan (1988) suggested
differential theoretical frameworks are rooted in the varying research methodologies, data
collection procedures, and deﬁnitions. The newness of the ﬁeld combined with
methodological limitations has led to an impasse of why violence occurs, who are the
victims, and violence characteristics. Violence is a difﬁcult and elusive topic to study and
this has compromised traditional research methodologies. Therefore, theorizing about
intimate partner violence is based on the conclusions of limited methodologies.
This dissertation will approach intimate partner violence research with a new statistical
technique to erode existing research barriers. The methodological technique, capture-
recapture, is adapted from wildlife and animal researchers to characterize the population

of violence between intimate partners. This study will demonstrate how the new

statistical procedure will open up the theoretical development of the study of violence

perpetrated by intimates.

11. Literature Review
A. The Major Theoretical Perspectives

Disciplinary theoretical development has been inﬂuenced by the diversity of
approaches to intimate partner violence. While there is considerable strength in
approaching a social issue from a multidisciplinary perspective, there has been no
synthesis regarding this subject (Gelles and Loseke, 1993; Ohlin and Tonry, 1989;
Steinman, I991). The ﬁeld of sociology and family studies in speciﬁc began to focus on
“family violence” (Straus, 1971; Gelles, 1974) just at the time functionalism was being
questioned and dismissed as a research conceptual framework. The politically tumultuous
era of the Vietnam War, the Civil Rights Movement, and consequently the Women’s
Movement were part of the catalyst for theoretical change in Sociology. Family
sociologists were some of the ﬁrst academics to look at violence and therefore, their
theoretical perspectives dominated the world of academia (Yllo, 1993). These
sociologists, led by Murray Straus and Richard Gelles in the early 70’s, conceptualized
family violence as a form of conﬂict. Like other sociologists of their time, Straus and
Gelles bypassed ﬁmctionalism and turned towards conﬂict frameworks to explain
violence. Both Straus and Gelles have restated and revised their theories of violence but
still, conﬂict remains the basis for their now meta-level conceptual framework (Yllo,

1993).

Before family researchers began theorizing about violence, advocates for battered
women played a major role in understanding family violence. The advocate's position on
intimate partner violence is not based within any one academic discipline, but rather was
born out of the empirical perceptions of activists that women are subject to violence due
to patriarchal systems (Dutton, 1994). These frameworks (also known as the feminist
perspective) is a “label applied to a subgroup of individuals who can be found in any
discipline” (Yllo, 1997; page 24).

Research methods were inﬂuential in the formation of the two primary and often
opposing domestic violence perspectives. These two frameworks are extremely different
and rooted in the fact of their different measurement and methodological approach.
Within each framework are multiple theories. The ﬁrst group of theories are referred to as
(l) the Family Violence Perspectives and the other are the (2) Feminist Persnectives
(Kurz, 1989). The Family Violence Perspectives focus on family systems while the
Feminist Perspectives focus on why men use force against women. ”There is no unified
feminist perspective on wife abuse” (Bograd, 1988. p 13) but rather there are common
themes found in the wide variety of feminist philosophies.

Family Violence theories are sometimes referred to as the Sociological
Perspective of Family Violence. However, several widely used sociological theoretical
developments are used to explain family violence. The commonality of the Family
Violence theories is that the focus is on the “family” and incorporates other forms of
violence such as elder abuse and child abuse. Family violence theorists traditionally were

Sociology of Family researchers with an interest in family violence.

The Feminist Theories focus on intimate partner violence and violence that is
perpetrated against women by men (Chapman and Gates, 1978; Dobash and Dobash,
1979;Martin, 1976; Pagelow, 1981; Russell, 1982; Schechter, 1982; Walker, 1979, 1984).
In addition, feminist theorists focus on the general trends of men using force against
women within historical, social, and cultural contexts. This chapter will highlight those
Sociological theories to be tested in this study, which also happen to be the most

dominant and the most heated debate regardless of disciplinary approaches.

1. The Family Violence Perspectives

Domestic violence research grew out of the research of family scholars who were
interested in a variety of family conﬂict issues. Straus (1971) and Gelles (1974) designed
a research agenda based on interviews regarding family violence. In 1975 and 1985,
national surveys of adult populations were used for the exploration of domestic violence.
By quantitatively analyzing the data, the commonalties were focused on for the Family
Violence Perspective. These researchers based their theory on the frequency of violence,
the roles of stress, and the norms that accept violence in some forms within the family

context. The major family violence sociological theories include:

a. General Systems Theory
Family violence is a product of the family system (Straus, 1973; Giles-Sims,
1983). The violence itself is not seen as a result of individual factors as many accepted

psychological theories suggested (Bersani and Chen, 1988). Straus (1973) modiﬁed

Scheff’s (1966) theory of family systems to explain family violence. Straus created eight

propositions of family violence (Bersani and Chen, 1988):

I Violence between family members has many causes and roots. Normative
structures, personality traits, frustrations and conﬂicts are only some.

I Much more family violence occurs than is ever reported.

I Most violence is either denied or considered normal.

I Stereotyped family violence imagery is learned in early childhood from parents,
siblings, and other children.

I The family violence stereotypes are continually reafﬁrmed for adults and children
through ordinary social interaction and the mass media.

I Violent acts by violent persons may generate positive feedback, that is, these acts
may produce the desired results.

I Use of violence, when contrary to family norms, creates additional conﬂict over
the original violence.

I Persons who are labeled as violent may be encouraged to play out a violent role,
either to live up to the expectations of others or to fulﬁll their own self-concept of
being violent or dangerous.

Both Straus and Giles-Sims (1973 and 1983) suggested that the established family system

could impact increases and decreases in the level of violence.

b. Resource Theory

Supporters of this perspective suggest that violence or the threat of violence is
always present in the family system. Violence is driven by the resources, or lack there of.
According to William Goode (1971) individuals within the family may use violence as a
means to problem solving when they are lacking in resources. Goode (1971) suggested
that family systems are power systems and that husbands can contribute more resources
to a marriage, giving him the dominant position. However, he also contended the
violence itself was inversely related to the amount of resources because as the assailant

increases his access to resources, the less he may need to force his partner (Bersani and

Chen, 1988). Goode’s theory predicts persons of lower economic strata are more likely to

use force on their partner (1971).

c. Exchange/Social Control Theory

Richard Gelles (1983) describes violence is controlled by costs and rewards,
meaning violence is used when the costs are fewer than the rewards. Furthermore, Gelles
suggests that because violence is socially sanctioned in our society many of the potential
costs have been removed.

Social control theory has frequently been used to explain juvenile delinquency as
it purports that committing crime is just a part of human nature (Nettler, 1978; Vold and
Bernard, 1985). Exchange theory assumes that every human act is either to gain rewards
or avoid negative consequences (Blau, 1964; Homans, I961). Gelles (1983) combines
exchange theory with social control theory in what he views as a middle range theory
such as Merton (1967) advocated. Gelles argues that the contribution of exchange theory
to family violence is family members will use violence if the negative consequences of
being violent are not greater than the beneﬁts. In addition, the contribution from
exchange theory to the explanation of family violence is the violence will occur without
sufﬁcient social controls in place. Gelles states, “People hit and abuse other family

members because they can” (1983, page 157).

d. Subculture of Violence Theory
This sociocultural explanation of violence posits there are certain subcultures

within our society where violence is more normalized than other sectors (Wolfgang and

Ferracuti, 1982). Wolfgang and Ferracuti (1982) ﬁnd violence is more based on a culture
than on social-structure. Therefore, certain subcultures will be more prone to violence
and will be acting as expected for that particular subculture. Violence is seen as

normalized within that group’s collective values.

2. The Feminist Perspectives

The feminist perspectives began with advocacy for victims of battering before
developing into a research theoretical framework (Dobash and Dobash, 1979; Martin,
1981; Roy, 1976; Walker, 1984). Theoretically, the feminist perspectives emphasize the
historical traditions of the patriarchal family, contemporary constructions of masculinity
and femininity, and structural constraints that make escape difﬁcult for women who are
systematically beaten (Johnson, 1995).

Curtis (1986) emphasizes that sociologically, authority is the most important
source of power and is the driving force of patriarchy. Ultimately, males have the
authority to control the family setting. Gender inequality is supported structurally.
Bersani and Chen (1988) stated the reluctance of social institutions to intervene and
prevent is reﬂective of the patriarchal structure. Martin (1976) found violence against
women is ﬁtting with patriarchy because “The economic and social structure of our
present society depend upon the degradation, subjugation, and exploitation of women”
(page 15).

Feminist theorists visualize domestic violence as a product of patriarchal
traditions of men's right to control their women. It involves the "systematic use of not

only violence, but economic subordination, threats, isolation, and other control tactics"

(Johnson, 1995: page 284). This violence is continuous physical, psychological and
intentional. Johnson (1995) who refers to this type of violence as patriarchal terrorism
states the "attention on the systematic, intentional nature of this form of violence and
forces us to attend routinely to the historical and cultural roots of this form of family
violence" (page 284). Clearly stated, subscribers of the feminist theories identify the
causes of domestic violence as rooted in the larger societal structure. While these
perspectives certainly cross disciplinary boundaries, the structural nature of the feminist
perspectives are in keeping with sociological tradition. The feminist theories are rooted in
a variety of philosophies, however, there are several constants. Bograd (1988) cited four
major commonalties in the feminist theories while acknowledging vast differences. Those

common dimensions are:

a. The constructs of gender and power

Feminist theorists view an act of violence within the social context and not as an
isolated or individual event. Patriarchy as a structural issue is seen as the strongest
underlying factor in woman battering at the personal level. Physical violence is an
effective means of maintaining domination of women by men. Furthermore, even those
males who are not personally violent still beneﬁt as a class from the restriction placed on

women.

b. Family as a historically situated social institution
The family must be examined within the cultural and structural context of a given

time and place. Woman battering is a common event and is NOT rooted in the breakdown

of family functioning. Rather, violence against women is normalized in a patriarchal
society where families are isolated and there is a greater division of private and public
life. Furthermore, strong genderized roles have developed that bind women to men
legally and morally (Breines and Gordon, 1983; Dobash and Dobash, 1979; Martin,

1976; Schechter, 1982) which reinforces the control men have of women.

c. Validating women’s experience

Feminist theorists assume that male domination inﬂuences everything from
behavior and attitudes to theoretical development. Under these circumstances, women’s
experiences may be seen as invalid. The feminist perspectives explain the experience of
battered women from their own frame of reference and critically examines other

theoretical development that incorporates victim blaming, minimizing, and devaluing.

d. Employing scholarship for women
The feminist theoretical development in violence against women originated in the
activism of the battered women’s movement of the early 70’s. To this end, feminist

scholarship is dedicated to the advocacy for women in addition to being the study focus.

B. Limitations of Theoretical Perspectives
1. Female on Male Violence

Research, conducted by Straus (1971) and Gelles (1974), supported the Family
Violence Theories. Results from their survey research suggested women and men are

nearly equal in their initiation of partner violence. Feminist scholars rejected the notion

men and women equally initiate violence because it was only women victims they were
ﬁnding at the domestic violence shelters, in the hospital emergency rooms, and in the
legal system. Straus (1971) and Gelles (1974) failed to measure the context in which
female violence is initiated. For example, a woman may strike her male partner ﬁrst if
she perceived herself facing serious harm that she would be unable to avoid (Browne,
1987; Jurik, 1989; Jurik and Gregware, 1989). In fact, a battered woman may kill her
partner when he is not attacking her (Browne, 1987). As Straus (1993) admittedly reports
“who initiates an assault and who is injured are important aspects of the contextual
information needed for a full understanding of the gendered aspects of intrafamily
assault. For example, there may have been an escalation of assaults throughout the
relationship with the original attacks by the man”. Ultimately, female to male violence
has been found to be much less physically injurious than male to female violence (Straus,

1986)

2. Conﬂict based

The family perspective is limited because it is based on Conﬂict theories which
do not characterize the gendered nature of conﬂict (Yllo, 1993). Instead of violence based
on a conﬂict of personal agendas, evidence suggests that the violence is a control tactic to
maintain the husband’s power (Bograd, 1988; Hanmer and Maynard, 1987; Jones and
Schechter, 1992, Ptacek, 1988). The conﬂict perspective also suggests purposeful
battering to gain resources or control or as a response to a situation when clearly, there is

evidence some males plan an assault in advance and look for an excuse afterwards

(Edleson, l 992).

10

3. Broad Generalization

The Family Violence theorists also do not envision spouse abuse as having a
distinct etiology from child abuse or elder abuse. Feminist theories are not generalizable
to all of family violence like the family perspective, however, there is insufﬁcient

evidence all forms of family violence should be analyzed jointly.

4. Ageism

Many researchers have speculated intimate partner violence decreases with age,
which is based on methodological ﬁndings (Pillemer and Finkelhor, 1993). Gelles (1993)
found that violence was primarily concentrated in ages 18-30. This assumption is based
solely on self-report, and therefore, mitigating factors are being overlooked. For example,
is it that violence has decreased with age or has the victim, over time, learned to
minimize physical attacks by backing down from confrontations or avoiding potential
confrontations by keeping quiet, submissive, and hiding. There is a large void in the
domestic violence literature addressing later life violence. In fact there is no evidence
declining rates of violence among older women are caused by a reduction in violence by
the male partner or an increase in desistance by the female partner. Also, older women
are less likely to be involved in relationships than younger women due to lower life
expectancy of males and the American tradition of marrying older men. In sum, there are
fewer males than females. The sex ratio of females to males increases with each older age

cohort (Demographic Yearbook, 1996).

11

5. Sampling Error

Finally, the family perspective is based on ﬁndings from large-scale national
surveys. Logically, the dynamics of domestic violence may largely preclude victims from
participating in surveys. Coercive control over women by their mates follows some well
documented patterns such as ‘Controlling what she does, who she sees and talks to, what
she reads, where she goes, limiting her outside involvement’ (Schechter, 1988). Women
who live under such a system of control and domination are not likely available for
sociology research studies. These victims are not represented in those family violence
surveys. Johnson (1995) ﬁnds evidence that the number of respondents who reported

using shelter services is far lower than percentage of females using shelter services.

6. Univariate Explanation

Feminist theory is limited because it uses only patriarchy to explain domestic
violence, which is a complex issue. Domestic violence may have multiple etiologies that
a more complex theoretical model could explain. Some feminist studies are beginning to
embrace more complex explanations of woman battering, but the progress has been Slow

in part by methodology.

7. Clinical Fallacy

Feminist research originated from the battered women's movement, the
perspective of these early researchers were traditionally based on observations of women
in shelters and emergency rooms. Feminist researchers often focus on smaller clinical

studies, which produce clinical fallacies. Research conducted in the shelters may not be

12

generalizable to the whole population although it may be a powerful framework to

describe the dynamics of violence and experiences of the population they serve.

III. Methodological Barriers Impede Theoretical Development

The methods are lagging behind recent theoretical advancements in the ﬁeld of
Sociology (Tickamyer, 1996) and without progress in the methods, the theory will not
self-actualize. For Sociologists, social reality and theory are closely tied to each other.
We derive our research questions from social reality and use theory to explain what we
ﬁnd. Methodology allows us to test our hypotheses to establish our theory creating an
intrinsic dependence. Theory establishes the demand put on the methods. Sociologists
theorize but are unable to critically examine theory with limited methods. If there is
theoretical development, the theories cannot be critically examined with limited
methodologies. Practitioners do not ﬁnd intimate partner violence theories reﬂective of
the social reality. These theories are difﬁcult to challenge without better methodologies.
As stated by Joseph Weis (1989), “insuﬂicient attention has been given to
methodological issues that need to be investigated and resolved before more valid and
reliable estimates of the prevalence and correlates of family violence can be expected. ”
The methods are intermediary between social reality and theory. Tickamyer (1996)
suggested the most critical shortcomings in the discipline of Rural Sociology were not in
theoretical validity, but rather the ‘problem lies more in the inadequacies of data
conceptualization, production, and collection.’ Methods encompass issues of sampling,
measurement, deﬁnition, techniques and operationalization. These shortcomings in

methodology have impeded development and testing of theory.

13

IV. Research Methodological Challenges in Sociology

Populations can be “hidden” from researchers because of unawareness or because
of covert or illegal behaviors (Hay, 1997). Population estimations also depend on the
methodology used and the accuracy and availability of the data (Hser et al., 1992;
Rhodes, 1993). Brecht and Wickens (1993) suggested a ﬁxed set of rules for population
estimation is inappropriate because the “reality of the research contexts varies and never
achieves a perfect ﬁt with mathematical models” (Barnes, 1995).

Due to difﬁculty in collecting and measuring information on covert and illegal
activities such as intimate partner violence, there is no one data source available for
completely accurate data on prevalence. The victims are hidden and their perpetrators are
involved in illegal activity (Browne, 1997). Neither a census nor a sample would capture
this invisible population. Traditional methodologies are limited in this scenario and
therefore, we turn towards a technique employed by wildlife researchers - - Capture /
Recapture (Boukhout, 1994; Schemnitz, 1980, Seber, 1993).

The Department of Natural Resources, responsible for estimating wildlife
populations, coined the term capture/recapture because they literally capture their
subjects of study (deer and other wildlife), release them, and capture a second sample.
Capture / recapture uses the information from the overlapping cases to estimate the
invisible cases that do not appear in any of the data sources (Bishop, Fienberg, and

Holland 1975).

14

V. Solution to the Problem

Women in physically abusive relationships belong to an invisible hidden
population (Browne, 1987); therefore, the limitations of violence research and their
problems with validity and reliability (Koss 1993; Johnson 1995) formed the problem and
the research questions to be analyzed for this study. Capture-Recapture is an option for
researchers who have been unable to identify invisible populations. By using Capture-
recapture, we enhance our statistics and establish robustness. Capture-recapture will
allow for the development of theory by providing a population size. We cannot examine
all parameters of intimate partner violence and elicit a developmental pattern unless we
can establish the sample ﬁrst. This study will establish a viable and appropriate technique
necessary to test hypotheses and therefore, support the theoretical development and
reﬁnement. A false positive or a true negative will mislead the researcher’s conclusion
and lead to erroneous theorizing. Methodological outcomes are extremely inﬂuential in
providing a framework in which to develop theories by testing hypotheses based on

social observations.

VI. Research Signiﬁcance

This study will explore creative new methodologies to be implemented by
Statistical Demographers for counting invisible populations. Before sociologists can
qualitatively examine the structural causes and implications of an issue such as intimate
partner violence to develop theoretical frameworks, they must ﬁrst be able to identify the

victims and persons at risk. The prevalence of spouse abuse among couples cannot be

15

derived from face to face interviews or any other formally structured interview. Due to
the nature of the topic, as will be discussed in great detail, people are generally reluctant
to admit they are victims of domestic violence due to fear, loss of status and
embarrassment.

There are many elusive and hidden populations that need to be counted to
establish their social signiﬁcance. Two recent examples of the practical application of
capture / recapture research were on prostitution (McKeganey et al. 1992) and
homelessness (Fisher, et al. 1994). The capture / recapture technique is being explored in
epidemiological research, however, has rarely been applied to social research, and never
in estimating the prevalence of victims of intimate partner violence.

The application of this technique in sociological research pushes the general
knowledge about demography ahead. This use of the capture / recapture technique is
taking an old technique and utilizing it in a novel manner for sociological research. This
use of the capture / recapture will provide a precedence for social researchers by
providing them with a new method of indirect estimation. In fact, this methodology can
be used when social scientists have found enumeration to be impossible. This technique
could create a paradigm shift in the way researchers do their counting by providing
widespread, accurate, and cost effective means to estimate the size of certain populations
(LaPorte 1994).

This methodology will open up the framework for theoretical development and
may change how we approach domestic violence. This research increases the “body of
sociological knowledge” by expanding our conception of domestic violence and by

establishing the persuasiveness of intimate partner violence, who the victims are, and

16

their characteristics. This technique can help to test existing theoretical frameworks of
violence between intimates.

This study will begin to look at the impact violence has on older populations as
compared to younger populations. Although, detailed information surrounding the abuse
of the older woman is beyond the scope of this study, we may see the incidence of
violence among the elderly is much greater than found in previous research. We will see
the frequency older victims of intimate partner violence present themselves to police
departments, prosecutors, domestic violence shelters, and emergency rooms.

This research provides a framework for the beginning of sociological theory on
intimate partner violence according to age. This topic is timely because this country’s
average age is quickly rising. Soon, the baby boomer age cohorts will reach the elder
years and Michigan (and The United States) will have a disproportionate number of
senior citizens (Ofﬁce of the State Demographer, 1995). Domestic violence among the
elderly is of great importance when so many Americans are in the older age brackets
(Ofﬁce of the State Demographer, 1997) and are still victims of intimate partner violence.
Based on the current American population structure, intimate partner violence among
older couples will be even more of a social problem in the near future because there will
be more “at risk” women.

This study will determine if men are as likely to be battered as women and if there
is supporting evidence that women are as likely to be perpetrators as men. Determining
the gender role in violence will resolve the conﬂict between the feminist theorists and the

family violence theorists.

17

 

This research provides a departure from traditional enumeration methods.
Historically, demographers approach to counting human populations is to count and
classify every person of interest (LaPorte, 1994). This study will demonstrate how it is
better to take an incomplete list of accurate information for population estimation than
broad based inaccurate data as in a census or a large scaled survey.

This research serves as an evaluation tool for service providers of victims of
domestic violence by determining the percentage of women missing from their registries.
Furthermore, this research will demonstrate the overlap and dependencies between
services of the various agencies. There are increasing trends for communities to combine
the efforts of multiple agencies to reduce and prevent domestic violence and this research
will Show to what extent those agencies overlap. For example, shelters encourage women
to report their cases to the police departments and these results will demonstrate to what
extent women present to the different agencies. This information will prove useful in
program development and community collaboration to better help victims.

Finally, improving violence research methodologies is sociologically signiﬁcant
because it can establish “suggestions about how to reduce the extensiveness and severity
of social problems” (Zastrow, 1992). To this end, it is important to identify the special
needs of victims by identifying their characteristics and the etiology of intimate partner
violence. A more accurate depiction better prevents intimate partner violence and can aid

in the development of intervention programs by government and policy-makers.

18

CHAPTER 2 - METHODS AND TECHNIQUES

I. Research Application

There is substantial power of a research design built on multimethodology for
addressing signiﬁcant social problems like domestic violence. Traditional methods
cannot sufﬁciently estimate the magnitude of violence in our population. Therefore,
appropriate and creative techniques are required to evaluate effectiveness of control
strategies, to monitor changes in the nature and severity of domestic violence, to identify
additional research needs, and ﬁnally, to facilitate planning for prevention and
intervention strategies. This research bears tremendous social responsibilities in
effectively addressing the intimate partner violence (IPV) social problem. To this end,
interdisciplinary estimation techniques applied to epidemiological and ﬁsheries and
wildlife studies will be put to the challenge in this intimate partner violence research

study.

11. Research Questions

This study will involve measuring relative prevalence (number of victims within a
relative time frame) and incidence (number of assaults experienced by victims) through
the Capture-Recapture technique and will be used to test the following research

questions:

Research Question 1: Can the capture-recapture technique indirectly estimate the
size of an invisible population?

Research Question 2: Are there signiﬁcantly more cases of domestic violence than
are reported or estimated from surveys?

19

Research Question 3: Does older couple violence compare to younger couple
violence?
Research Question 4: Are women as likely to perpetuate violence as men?

Capture/recapture is an exciting new methodology that is promising to researchers
as a means for estimating the size of invisible and elusive populations. However, there is
a polarization of estimation researchers into two groups - — those who believe capture /
recapture is the all encompassing answer to demographic shortcomings and those who
ﬁnd the technique enticing as a cure-all but who nonetheless are skeptical about the
ability of the technique to accurately measure social phenomena (Hay 1996). LaPorte
(1994) contends capture / recapture will change how population estimation is conducted
in all disciplines. In contrast, Hook and Regal (1995) and Hay (1996) are more reluctant
about capture / recapture estimates due to the. unknown estimation precision of the
technique. This division in the literature of capture / recapture critiques may be
reconciled with simulations and statistical controls.

To answer the ﬁrst research question, a feasibility study will be conducted on
capture-recapture. The study will include a demonstration of how the statistical process is
able to indirectly estimate a population size and whether the technique is viable outside of
a theoretical model. A simulation study will be used to test the sensitivity of the
technique by extracting random numbers from a matrix and imputing them into sample
size and duplication cases. From the Simulation it will be possible to demonstrate how
close the capture-recapture estimates come to a known population size in a controlled
experiment.

The simulation will produce a distribution of the population estimates derived

from capture/recapture in order to predict how close the estimates lie in relation to the

20

known population size. The simulation model will demonstrate what happens to the
estimates with varying probability of being captured and varying overlapping of sample
sizes. The simulation model will convey how “sensitive” the capture-recapture equation
is to sample size. Finally, the simulation will be used to estimate the precision for
independent models.

To answer the second research question, current domestic violence rate estimates
will be compared to the rates derived ﬁ'om the Capture / Recapture technique to
determine if there are signiﬁcantly more cases derived from the new statistical technique.
We assume the capture / recapture technique will yield an estimate closer to the true
population size than those derived from single sources or from surveys. Therefore, if the
capture / recapture estimates are larger than previous estimates, we will assume that
indeed intimate partner violence affects a larger portion of the population than previously
suspected. .

Since there is no way to know how many persons are victims of intimate partner
violence, current statistics are derived from surveys. Victims remain invisible in research
because they refrain from self-identiﬁcation in surveys and ﬁeld studies (Pillemer and
Finkelhor, 1988; McPherson, 1990; Vinton, 1992). For comparative purposes, rates will
be derived from the Violence Against Women Study conducted by The Gallup
Organization for the state of Michigan in 1996 and also from the National Family
Violence Survey and the National Crime Victim Survey.

The third question will be answered by comparing the prevalence of intimate
partner violence between older and younger women to see if there is a signiﬁcant

difference in rates of abuse. In addition, the capture-recapture technique will be used to

21

determine if older women are more invisible than younger women from institutional
registries. This will be determined by estimating the prevalence according to age and
ﬁnding the proportion of observed or “captured” women according to age. The
proportions between older and younger women will be compared to determine what
proportion of the population is not accounted in the estimations.

Finally, the prevalence of female-on-male and male-on-female violence we be
compared to determine gender differences. Again, the capture-recapture technique will
also determine which gender is more elusive to the prosecutor’s office, police

departments, hospitals, shelters and outreach programs for Marquette County.

111. Operational Deﬁnitions

Intimate Partner Violence is the threatened or actual intentional use of physical,
sexual and/or psychological/emotional force against a person. This includes the physical
and emotional assault or stalking of a woman by former or current partners. Commonly
referred to types of behavior that ﬁt within this deﬁnition include domestic violence,
interpersonal violence, intimate partner violence, partner violence, wife battery, spouse
abuse, marital rape, stalking an intimate, violence in a dating relationship. For purposes
of this research study, only physical violence will be measured because these data are
based on physical evidence of violence. However, in no manner should it be inferred that
by excluding emotional and psychological violence from this study those non-physical
forms are any less traumatic or more humane to the victims. Verbal Aggression may be
more damaging than physical attacks (Vissing et al., 1991). “One can hurt a partner

deeply — even drive the person to suicide without lifting a ﬁnger (Straus, 1993; page 68).

22

The exclusion of non-physical violence from this study indicates a limitation of
measurement capabilities and an area for further research in the future.

Intimate Partner Violence (IPV) is often interchanged with domestic violence or
spouse abuse, however, it includes the forms of domestic violence as described above.
The “intimate” indicates current or former relationship of a sexual nature. The term
intimate partner violence is preferred to domestic violence because it encompasses
victims trying to leave their partner. Also intimate partner violence categorizes similar
types of violence that may be excluded when only focusing on wife battering or spouse
abuse.

Older women are considered all women over the age of forty years for this
research study. Forty and older have been selected as an inclusion criteria because
dichotomizing the population at this age still allows for sufﬁcient sample size in the older
category while still distinguishing a difference between women in their child-bearing
years verses women with completed fertility. Women with small children are generally
the preconceived “typical victim” of domestic violence and face obstacles speciﬁc to
their age group. This study seeks to also identify the nontraditional victims of domestic
violence to see if patterns and structures exist in this age cohort like their younger

counterparts.

IV. Capture / Recapture
The Capture-recapture method is derived from the practice of randomly sampling
a deﬁned population, marking the captured sample members for later identiﬁcation

purposes, then releasing those captured back into the population. A second random

23

sample from the same population is taken and the proportion of marked individuals from
the ﬁrst sample found in the second sample is assumed to be the same as the prOportion
of marked sample members in the deﬁned population (Barnes et al. 1995). Multiplication
of the two sample sizes divided by the number found in both samples results in an
estimate of the total population of interest (Bishop, Fienberg, and Holland, 1975).

The strength of capture/recapture is that while it adjusts for any individual source not
containing all cases, it generally assumes that the cases a source does contain are truly
cases. According to Hook and Regal (1995) Capture — Recapture has been applied to
human population research for four major applications. First, to estimate population size
when there is clearly incomplete data available from two or more sources. Second,
reﬁnement of estimations derived from surveys. Third, evaluation of registries; and
fourth, deriving plausible upper or lower limits on the total affected population in
conﬁdence intervals. The Department of Natural Resource methodology was justiﬁably
used for the four aforementioned reasons in the proceeding literature. (Abeni et al.1994;
Alho 1990; Barg and Huether 1983; Benn et al.1975; Bishop et al. 1975; Bloor et al.
1991; Bobo et al.; Brecht and Wickens 1993; Bruno et al. 1982; Chapman 1983; Chiue et
al. 1993; Cochi et al. 1989; Davis et al.1993; Doscher and Woodward 1993; Drucker and
Verrnund 1989; Espeland et al. 1988; Fisher et al. 1994; F rischer 1992; Frischer et
al.1991 ; Goldberg and Wittes 1978; Gutteridge and Collin 1994; Hartnoll et al. 1985;
Hewitt and Milner 1970; Hilsenbeck et al. 1992; Hook and Chambers 1980; Hook et al.
1982; Hook 1993; Hook and Regal 1992; Hser 1993; Huether et al. 1981; Kehoe et al.
1992; Kozinetz et al. 1993; Laporte et al. 1992; Lewis and Hassanein 1969; Lie et al.

1994; Mastro et al. 1994; McCarty et al. 1992; McKeganey et al. 1992; Modesitt et al.

24

1990; Neugebauer 1984; Newmeyer 1988; Palfrey et al.1994; Prevots et al. 1994; Robles
et al. ; Rubin et al. 1992; Sachs et al. ; Schouten et al. 1994; Serrano Rios et al. 1990;
Sutter et al. 1990; Sutter and Cochi 1992; Taylor 1989; van Haastrecht et al. 1991; Walter
et al. Watts et al. 1994; Wickens 1993; Wittes 1968; Wittes and Sidel 1968; Wittes et al.
1974; Woodward et al. 1985; and York and Madigan 1992). Neugebauer and Wittes
(1994) described the Capture-recapture method as helpful in that it “openly
acknowledges that data collected on a regular basis leaves out a large proportion of the
population of interest”.

In one of those epidemiological studies Mastro et al. (1994) utilized the capture /
recapture technique to estimate the number of injection drug users in Bangkok. Until this
research project was implemented, public health workers in Bangkok suspected much
higher rates of heroin use than were detected in survey data and/or institutional data.
Higher rates were suspected because public health researchers were able to determine the
percentage of heroin users who were HIV positive. The number of HIV cases increased
more than the reported number of heroin users. Capture-recapture was used by Mastro et
al. to count those cases missed by direct estimation procedures. Using the capture
recapture technique, an additional six thousand heroin users were identiﬁed. These results

reﬂected the increase in HIV cases that were known to be contracted from heroin usage.

V. Capture / Recapture in Wildlife Population Estimation
Using the example for estimating the number of deer in a designated area, a
sample of n1 deer are captured, tagged, counted and released back into the woods. A

second sample of deer, n2, are then caught. The number of recaptured (m) deer is counted

25

and is also known as the overlapping population. The proportion of tagged deer in the
second sample is m/nz which is assumed to be the same as the proportion of the sample to
all of the deer in the whole forest, n1/N. Thus, the number of deer in the whole forest, N,

is estimated (N eugebauer and Wittes 1994) as':

N=(n1*n2)/m

For example, if 100 deer are captured at Time I, and released and then 100 more
deer are captured at Time 2. Five of the deer at Time 2 also had been captured at Time 1,
meaning that 5% of the population from Time 1 was recaptured at Time 2. The
proportion of recaptures at Time 2 represents the proportion of the Time 1 sample to the
whole deer population. Thus, we can summarize the 100 deer captured during Time 2
equal 5% of the entire deer population. Therefore, we can estimate the total deer

population to be 2000.

N = (100 *100)/5 = 2000

Members of a population are “captured” by appearing in one data source or “list”
and are “recaptured” by appearing again in another list, or by “matching.” They are
“tagged” by virtue of having an identiﬁer where they can be traced from one “list” to the
next. The “lists” are matched against each other using the unique identiﬁer and the
matches between two lists and three lists are then counted m. Using these numbers and

the formula referenced above for a two-source estimation of population (Geiger and

 

' This equation is based on the assumption of independence.

26

Werner, 1924; Sekar and Deming, 1949), the number of the total population of IPV
victims can be estimated.

There are some rare events when demographers used capture / recapture in the
distant past. Currently, this technique is not in mainstream demography, however, is
being reintroduced to the ﬁeld because of its unique ability to calculate indirect
population estimates. In 1949, Sekar and Deming used the capture/recapture method to
estimate birth and death rates and the extent of registration. Their paper may be regarded
as the ﬁrst serious application of the capture-recapture method to human health, and
provided a good discussion on some of the practical problems associated with the
method. Shapiro (1894) applied the technique to birth registration in the United States,
using census data. By taking another source in addition to the census, the capture-
recapture method was used for estimating undercounts in vital statistics. The census of
1950 utilized capture-recapture to estimate the undercounting (N anan and White, 1997).
It was referred to as ‘dual system estimation’ (Nanan and White, 1997; page 145). This
system has also been used in the following census counts as part of the “post-enumeration
survey” to estimate the undercounting and the relative under-enumeration of particular
minority and poor groups (Nanan and White, 1997; page 145). The US Census Bureau
has proposed using capture-recapture as part of its statistical sampling and analysis for
the 2000 count because it will reduce costs. The US Census has also cited, as its rationale
for using this technique, that the US population is not a small sedentary population where
a door-to-door survey is more appropriate. Reluctance to use capture-recapture for

estimating the undercounts has faced barriers not in the methodology, but rather in the

27

political ramiﬁcations of reapportionment of House of Representative seats (Nanan and

White, 1997).

VI. Capture / Recapture Applied to Marquette County

Figure 2.1 Two Sample Database Overlap

 

 

 

\ J

The simplest capture-recapture model is the so-called two-source model, applied
to estimate the unknown size of a population. The ﬁrst source (A) provides the
individuals for marking or tagging and is returned to the population (rectangle), while the
second source (C) provides the captures at Time 2. Using the numbers of individuals
caught in both sources (B) (the recaptures) and the numbers caught in just one source (A-
B or C-B), it is possible to estimate the number not caught in either source(D), thus
providing an estimate of the total population size, N.

The capture-recapture method can, in principle, be applied to any situation in
which there are two incomplete lists (International Working Group for Disease

Monitoring and Forecasting, 1995). One Simply replaces “being caught in source (A)” by

28

“being on list (A).” This is the case in Epidemiology where lists can be constructed from
a variety of sources such as hospital records, doctors’ medical ﬁles, medical
prescriptions, and so on. These lists are incomplete by their very nature, and the problem
is to estimate those missing from both lists. Incomplete list estimation, (also known as
incomplete case ascertainment), is an excellent scientiﬁc method borrowed from wildlife
ecologists and public health researchers.

Capture-recapture is perfectly suited for indirectly estimating the prevalence of
intimate partner violence in this dissertation. Victims of intimate partner violence are
elusive and are not exhaustively reported to any one institution. However, there are
several agencies where cases of intimate partner violence ARE reported. These lists are
merely “incomplete” albeit true. For example, the women who report to domestic
violence agencies are true cases of intimate partner violence, however, not all women
seek Shelter after violent encounters with Signiﬁcant partners. Therefore, the list of cases
from a shelter is said to be “real cases” as well as incomplete. Capture-recapture is
applicable in situations where missing cases are a factor. Capture-recapture can
operationalize the overlap of two or more “incomplete” lists of data as long as the cases
are identiﬁable and the number of cases per list is known.

Applying this technique to the Marquette population, every case (N) of intimate
partner violence is located within the rectangle. This includes cases reported in the
medical reports, police reports, shelter cases, and outreach cases, AND those cases that
were never reported. A and C, the lists according to institutional data sources, will link
identical cases together through identiﬁers (ﬁrst and last name and/or address). Those

cases that are linked (B) will be used to estimate the unknown cases (D).

29

There is an alternative method for estimating the invisible population by
arranging the observed data in a 2 by 2 table with one missing cell (Fienberg, 1972).
Estimating the missing cell using contingency tables lends itself well to increasing the
number of data sources and using more complicated models (as will be discussed in
greater detail in Chapter 4). The invisible population is then added to the observed
population to estimate the total population of a given phenomenon. This technique was
independently created by two different researchers, Petersen (1896) and Lincoln (1930),
because it is so intuitively logical. Hence, the technique is often referred to as the

Petersen estimate or the Lincoln index (Fienberg, 1972).

VII. Satisfying the Necessary Assumptions for Capture / Recapture

For applying the capture-recapture estimation method, several assumptions are
required.
Assumptions:

1. There is no change to the population during the investigation (population
stability).

2. For each source, each individual has the same chance of being included in the

source (catchability).

The two sources are independent.

4. Positive identiﬁcation of true cases and accurate matching.

DJ

Continuing with the discussion of the capture-recapture method from the two-sample
model with sources 1 and 2. This example taken from the lntemational Working Group
(1995) assumes that m“ is the number of individuals captured in both sources, m2; is the
number of individuals un-captured in either source, and ml and mm are the numbers of

individuals captured in only one source. Therefore, “m1 1+ m21+m12” is the number of

30

different individuals captured in two sources. Furthermore, assume that each individual
has an equal probability of being captured; each individual has p1 of being captured in

source 1, and p; in source 2. Therefore, the expected numbers of being captured in two

sources are:
E(n1) = N * p. Equation 1
E(n2) = N * p2 Equation 2
E(m11) = N * p12 Equation 3

Figure 2.2 Contingency Table of 2-Source Capture-Recapture

 

 

 

 

 

Source 2 Total
captured un-captured
Captured mm "112 n1= mil + le
Source 1
un-captured m2] mg;
Total n; = mu + mzr N: mn+m21+m12+ M22

 

 

 

 

 

 

 

If we assume that the proportion of source 1 for the whole population is roughly
the same as it is in source 2 (which is based on the assumption each individual has the
same chance of being included in the source), then (nl/N) = (m 1/ n2) and therefore the

basic idea of capture / recapture (Petersen, 1896, Barnes 1995, Mastro 1994) is:

E(N) = n1 * n2 / n11 Equation 4

31

Simply stated, the expected total number of individuals is a function of the size of
the ﬁrst source and an adjustment factor, that is the inverse of the estimated level of
ascertainment by the ﬁrst source (IWG, 1995). Further equations can be derived from the
original capture/recapture equation as derived in the lntemational Working Group for
Disease Monitoring and Forecasting (1995). Another way of writing this result, which is
useful in the log-linear formulation described later (to adjust for an assumption violation),

is
E(N) = (mm + "121+ "112) + E("122), where E("122) = ”'21 * "112 / mu.

Following this logic, equation four can be further transformed into:

E(N)=(N*P1)‘(N*P2)/(N’P12)=N*PI*Pz/Plz Equati0n5
A. Source Dependency / Independence

If the two sources are independent from each other, the degree of dependency, R=
(p1 * p2 /p12), should be equal or very close to 1, and then the expected/estimated N
Should be unbiased, equal or very close to the true total population size. If the two

sources are dependent,

R =p1 I"p2 /p12 =p2 /p2“ Equation 6

32

where p2“ represents the probability of an individual being in the second source given
that she is in the ﬁrst source. If being in the ﬁrst source tends to increase the probability
of being recaptured, then p2“ > p2, and R should be less than 1, and the estimated N will
underestimate the true N. Similarly, if being in the ﬁrst source tends to decrease the
probability of being recaptured in the second source, the estimated N will be upward;
over-estimated.

In the case of Marquette, the violation of the assumption of independence must be
resolved. For example, there is dependency between medical and police ﬁles. Victims of
abuse who have sustained injuries requiring treatment may present at the hospital. Health
Care workers are required to report abuse cases to the police. While the victim did not
report the incident directly to the police, the police become involved and ﬁle a report
after being called in by the medical staff at the hospital. In this case, being captured in the
police data is dependent on being captured in the medical data.

More technically stated: Any two sources A and C are independent if the overall
probability of members of a population who appear in their intersection P(A and C) or the
overlap (B) is equal to the product of the average P(A *C)/ P(A and C) probabilities of
appearing in both A and B. When A and C have no cases in common whatsoever, then
the probability of being in both of them is null. In contrast, if all of the cases of one data
source are found in the second data source, then the probability of A (ﬁrst data source)
and B (overlap) being the same is 1.0. Dependency tends to produce “underestimates”
(Hook, 1995). The assumption of independence may be tested with the use of log-linear
techniques applied to multiple sample Capture-recapture models (Fienberg, 1998;

Frischer and Leyland, 1992; Hser, 1993; Bishop et al., 1975).

33

Although independence must be sufficiently addressed, this proposed research is
using three-fgctor canture-regmture in contrast to two-factor capture/recapture. When
using the three-factor (lists) “the assumption of independence can be dropped, and
interdependence among data sets can be accounted for by using Log-linear modeling
techniques to assess source dependencies” (N anan and White, 1987; page 145).
Furthermore, when the number of cases contained on each list is large, the estimates are
less sensitive to dependency of samples and catchability (Hook, 1995). However, for
further explanation of controlling for violations of the necessary assumptions, see

Chapter 4.

B. Population Stability

The third assumption is also controlled for by the catchability statistical controls
because remaining in a population makes a case more catchable than one which is
initiated by a person who has left the population. There are no populations that remain
unchanged during the research period. Therefore, population stability is identiﬁed as the
degree of “instability”. Theoretically, there is constant out-migration and in-migration
births and deaths; however, as long as the overall population size, calculated within a
given time frame (1996), remains fairly constant, there is equal opportunity for the loss of
perpetrators as well as in-migration of new perpetrators (given the example of domestic
violence).

The samples used for this study were collected simultaneously which reduces the
risk of violating the population stability assumption. If the samples were taken

sequentially, which is the case in wildlife research, a sample is taken during one time

34

period and released. At a later time, a second sample is collected. There is room for
inmigration, outmigration, births and deaths between the two sampling periods. In
contrast, this research study examines data from various samples during the same time
period. Therefore, even if there was some entering and exiting of captured persons, those
persons still had the possibility of being captured in more than one sample. In the case of
this research, three-factor capture recapture is being used and therefore, as described

above, it is possible to install log linear controls for sample dependencies.

C. Catchability

The probability of ascertainment varies by any of the institutional sources.
Catchability can be inﬂuenced because of geographic or socio-economic variables (Hook,
1995). The data must be modeled (similar to independence log-linear analysis) and tested
for deviations from independence. Overall dependency or relative bias estimates can be
explained as though they were calculated from sources with no variable catchability
(Hook, 1995). Because the medical, Shelter, and police database contain some data on
perpetrators and victims of violence, it will be possible to control for likely causes of
catchability. Items such as “age” can be used to estimate the population according to
strata. If there are large differences between subgroups, the estimates can be calculated

while adjusting for covariates.

D. True Cases and Accurate Matching

The technique of capture-recapture can only be applied in situations where there

are known cases of the topic of interest. Although it is absolute that the data source is

35

incomplete, those cases in the database must be accurate. Furthermore, the cases must

have sufﬁcient identiﬁers to positively match all cases between data sources.

VIII. Validation of Capture / Recapture

Generating a Simple capture / recapture estimate as a true population size does not
stand alone as a valid measure of violence prevalence. All measurement is to some
degree indirect and imprecise. When we try to observe a given phenomenon or behavior,
we invariably must rely on indicators that are imperfect in two ways: at the level of
conceptualization and at the level of measurement.

Even if we agree at the conceptual level on how to deﬁne abusive behavior, our
actual measurements and indicators (validity) of such behavior are subject to error. For
example, information about an individual's past record of Spousal abuse may come ﬁom
an unreliable source, may be missing from ofﬁcial records, or may be incomplete,
inexact, or unveriﬁed. Thus, there is a certain risk that actual perpetrators will not be
"captured" (or the individual may have been "captured" but there was insufﬁcient
evidence to demonstrate conclusively what was the nature or severity of the event or
behavior). Furthermore, we may only have circumstantial evidence or trace evidence that
a given event occurred; we may observe some of the consequences of some action but not
the action itself. Because of the imperfections of records and available information, we
need to be especially concerned about relying only on a Single source of information. In
addition, any single indicator of a complex phenomenon is likely to reﬂect only some

aspect of that phenomenon.

36

Single indicators of intimate partner violence are invalid measures because of
these threats of validity. Capture / recapture uses multiple sources and is an improvement
in itself of these types of measurement error. However, we must demonstrate that capture
/ recapture is not only an improvement of “invalid” measures of violence, but is indeed
‘a valid measure’. Capture / recapture is not sensitive to datasets containing missing
cases, in fact it is a technique that adjusts for incomplete case ascertainment.

Scientists have long understood the importance of making multiple trials and
experiments in order to test their hypotheses (reliability). Furthermore, because of the
need to rely on indirect evidence and imperfect information, they usually seek to test their
hypotheses using multiple methods and multiple indicators. The more a researcher is
able to verify the phenomenon using multiple indicators and different methods, the more
conﬁdence can be placed in the observations. That is, the more valid the inferences or
conclusions that are derived from empirical research, the more certain they can be of their
conclusions. We often seek validation or corroborating evidence from second or third
sources before we take action or draw frnal conclusions. For this reason, it is important to
seek multiple and independent sources of information to verify that what we are
observing is true and thus increasing the reliability of the methodology.

King et al. (1994) emphasized, "various ways in which we can increase our
leverage over a research problem. The primary way is to increase the number of
observable implications of our hypothesis and seek conﬁrmation of those implications.
Maximizing leverage is so important and so general that we strongly recommend that
researchers routinely list all possible observable implications of their hypotheses that

might be observed in their data or in other data."

37

Capture / recapture in essence is a form of methodological triangulation by
calculating estimates from a variety of data-source combinations. In fact, Fienberg (1998)
advocates proﬁling possible data combination capture-recapture conﬁdence intervals for
comparative purposes. There have been studies where the actual size of the population
was known, however, capture / recapture was utilized on sub-populations to estimate the
overall population (Hook, 1982). There is empirical evidence that using three or more
sources provides reasonable estimates of the total population. Mastro (1995) found that
when capture / recapture used at least three factors, the estimates were near that of known
population sizes, while controlling for necessary assumption violations.

There has also been evidence that using the median estimate of a variety of source
combinations provided a form of validation for the ﬁnal estimation (F rischer et al., 1993).
Intemal validity is checked by comparing the estimate of one source, derived by
assuming the other two are independent. For example, if we calculate prosecutor source
based estimates, while assuming the other two (shelter and outreach) are independent.
The estimate of only prosecutor source is used in a ratio with an estimate created only by
the shelter and outreach. The ratio is an estimate of the relative bias of the three source
estimate (Hook, 1995). Multiple source log-linear analyses that produce consistent results

are more evidence of a valid estimate as will be clearly demonstrated in chapter 4.

IX. Relational Databases for Capture/Recapture Analysis
Capture / Recapture requires the use of “relational database analysis” as opposed
to analysis on a ﬂattened ﬁle. The major difference between ﬂat and relational databases

is the structure of data storage. The nature of relational databases enables them to link to

38

each other based upon one or more key variables. As you see below, the set of relational
databases is linked together based upon three variables, social security number, date of
incident, and data source. Here we use social security number for illustration purposes.
Most social researchers use ﬂat databases for analyses as pictured below. However, for
purposes of capture / recapture the data must remain desegregated based on the referring
source. Cases of intimate partner violence will be linked together according to identiﬁers
(such as social security number or name) as shown in the relational databases below2 (See
Figure 2.2). When a set of relational databases is combined into a ﬂat database it appears
the ﬂat database contains all the records because every incident is listed once. However, a

part of information has been lost.

 

2 Database illustration was created by Chun-Hao Li for ‘Estimating Incidence of Family Violence in the
USAF” by Wibert and Li, 1997.

39

Figure 2.3 Flap VS. Relational Database

Flat Database

8813 Date of Incident
000-00-0001 01/01/97
000000-0002 01/15/97
000-00-0002 _,02/01/97,
000-00-0003 : 01/06/97
000-00-0003 : 02/05/97
000-00-0003 ii 02/28/97
000-00-0003 ; 03/10/97
000-00-0904 ,01/07/97. .
000-00-0005 . 02/01/97
000-00-0005 ‘ 02/10/97
000-00-0005 02/15/97
000-00-0006 02/15/97
000-00-0006 ‘ 02/20/97
000-00-0007 . 01/20/97
000-00-0007 2 01/25/97
000-00-0008 02/20/97
SS#
Relational Databases 000000002
000-00-0003
SS# Date of Incident Source 000—00-0003
000—00—0001 > 01/01/97 > _ A 000000004
000-00-0002 01/15/97 A 000-00-0005
000-00-0002 02101/97 A 000—00—0007
000-00-0003 01/06/97 A
00000-0003 02/05/9‘7" ’ ”A '
000-00-0003 02l28/97 A SS#
000-00-0003 03/10/97 A coo-00.0001
000—00—0005 02/01/97 A 000-00—0003
000-00—0006 02/ 1 5/97 A 000-00—0005
000-00—0006 A

02/20/97

\ 000000005

40

Source

0003>>OO>ID>>>>'>>>

Date of Incident
01 / 1 5/97
02/05/97
03/10/97
01/07/97
02/01l97
01/20/97

Date of Incident
01 /01 /97
02105197
02/ 1 0/97
02/15/97
02/20/97
01 /25/97
02/20/97

Source

WWWWW

B
Som'ceB

Source
C

000000

By aggregating data into ﬂat databases, a piece of very important information for
the capture-recapture method is lost. In the ﬂat database, only one data source is entered.
The second and other data sources have never been identiﬁed in the database. For
example, from the ﬂat database, we are unable to tell that the incident which happened on
01/01/97 by the person, 000-00-0001, was also captured in both data sources A and C. As
the ﬁgure shows, a set of relational databases looks more complicated and less organized
than the ﬂat database, however, relational databases store the complete information for
the estimation capture-recapture method. Furthermore, based upon several key variables
or identiﬁers such as name and address, the same records which appear in the different
databases can be linked together. In short, the ﬂattened database appears to contain all the
records, however, to apply the capture-recapture method to estimate prevalence of
intimate partner violence, the ﬂat database is inappropriate and the relational databases

broken down by the data source are necessary.

X. Population of Interest
The intent of this multi-methodological approach is to ﬁnd prevalence and to

identify the trends and nature of intimate partner violence in Marquette County.

A. Marquette County, Michigan

Marquette is the largest county east of the Mississippi River (1,841 square miles).
It is located in the Upper Peninsula of Michigan on Lake Superior where the average
snowfall ranges from seven to twelve feet per year (Hayse et al., 1998). The 1990 Census

shows a total population in the county of 70,887. The city of Marquette, which is the

41

largest in the Upper Peninsula, has a population of 21,977. Northern Michigan
University, with a population of 8,000 students, is located within the city.

The terrain varies from the ancient hills of the Huron Mountains in the northwest,
to the extensive swamps and forests of the southern sections. The county has nearly 2,000
lakes and ponds, with 4,000 miles of rivers and streams. There is only one short stretch of
divided highway. The majority of roads are old two lane county roads. There are 47 small
isolated rural villages and cities with less than 1000 people (Hayse et al., 1998). Forty-
three percent of the county population is designated rural.

K. I. Sawyer Air Force Base, which was a major employer of local people, has
been closed down in the last decade. Iron ore processing is the county’s largest industry
and employer. The University and a large maximum-security state prison are also major
employers. Education, health care, chemicals, lumbering, shipping, agriculture and
tourism are economically important too.

Factors related to the difficulty of addressing domestic violence in Marquette
include: The small-community atmosphere, where great care is taken to keep the crime
hidden; and a poor economic base, which promotes ﬁnancial dependence on an abuser.
The sometimes-hostile terrain and extreme weather conditions, coupled with the rural
setting and lack of transportation, can keep a battered woman isolated, adding to her fear

and dependence on an abusive partner.

42

B. The Study

This study comes from the violence estimation portion of Marquette Research for
Justice Violence Agencies (MR JAVA)3 funded out of the Violence Against Women Act4
fimds via the Michigan Department of Community Health (Hayse et al., 1998). Marquette
County was selected as the target population because of access to excellent data sources
including Domestic Violence Shelter, Intimate Partner Violence Outreach Services,
Hospital, Police, and Prosecutor data. Furthermore, the Department of Community Health
has selected Marquette County for pilot research projects involving hospital data, medical
examiner data and police/prosecutor data. The Michigan Department of Community
Health and the Center for Disease Control have funded this research project to be
completed in Marquette County making it convenient to also use the same data for these

analyses. Furthermore, there will be access to conﬁdential data with identiﬁers.

XI. Data

In estimating intimate partner violence experienced by women, institutional
records in Marquette County will be used as the samples of persons captured and then
recaptured. These records include domestic violence shelter reports, 911 calls, violence
prevention outreach program records, prosecutor data, and police/emergency room
reports. In this study a multi method approach will be employed, collecting quantitative

data from general sources as samples for the application of the Capture-recapture

 

3 See http://vip.msu.edw’mriavg’indexhtml for details of project.

‘ The Violence Against Women Act (VAWA), passed as part of the Violent Crime Control and Law
Enforcement Act of 1994, takes a comprehensive approach to domestic violence and sexual assault,
combining a broad array of legal and practical reforms and will improve the responses of police,
prosecutors and judges to these crimes, force sex offenders to pay restitution to their victims and increase
funding for battered women's shelters. And, under the Act, the authority of a "stay away" order obtained
against an abuser will no longer stop at the state line.

43

technique to establish prevalence and incidence. Also, qualitative data is collected on the
victims to provide further characterizing information.

The ﬁrst database is the prosecutor data The second database will be those
women who sought safety or went into hiding at the Marquette County Domestic
Violence Shelter - - Harbor House. The third database comes from a Marquette Outreach
program. Women come to the Outreach Program in order to receive counseling services,
secure ﬁnancial resources, and learn about the dynamics of power and control in order to
prevent entering into another violent relationship and/or returning to their former batterer.
The Outreach Programs are Similar to the Shelter Program except that Outreach is non-
residential. In Marquette County there are two Outreach Program offices. Those ofﬁces
reside in the towns of Ishpeming and Marquette.

This research project will also use criminal justice and hospital data. When a
victim presents in the emergency room, the hospital is mandated by law to report cases of
domestic violence within the same day to the appropriate police department. It is
impossible to obtain conﬁdential data from the two hospitals in Marquette County;
however, for this research, those data are collected by the reports which are made to the
police departments. In turn, the police are mandated to ﬁle all reports of domestics within
48 hours to the prosecutor’s office. In addition to reports made to the police department
by outside agencies, the police are mandated by Michigan Law to make an arrest if the
altercation is physical in nature. The ofﬁcer has 48 hours to ﬁle a report with the
prosecutor’s ofﬁce. These data are all substantiated cases of domestic violence that are
reported directly to the prosecutor’s ofﬁce, the police department, and/or the hospitals. In

addition to reports ﬁled at the police departments and reports of arrests, the prosecutor’s

44

ofﬁce also kept records of all 911 calls made to Marquette police departments. Those
cases that were substantiated are contained in the prosecutor’s database. The prosecutor’s
database are also referred as authorized cases, meaning there is sufﬁcient evidence of
battering to proceed with a trial. It will need to be detennined through analysis if these
data registries will be considered as independent sources or will be combined into fewer
sources. The data were collected within the same time frame from the various domestic

violence prevention agencies within Marquette County - - 1995-1997.

XII. Limitations

One limitation of this research project is that persons that tend to get caught in
these databases (enumerated) may be the more severe physical cases. For example,
persons with less serious injuries will not seek treatment in the emergency rooms. There
is no way to control for severity or intensity of injury; however, it iS unlikely that there
are women who were physically abused without being injured who presented at the
hospital or shelter. While the capture-recapture technique lends itself well to controlling
for dependencies, the severity of injury may not be controlled for without some form of

injury measurement and thus, the data cannot control for injury.

XIII. Summation

This research uses the capture-recapture methodology that is currently being used
in epidemiological studies for indirect estimation. This technique has never been utilized
for indirectly estimating the proportion of the population experiencing intimate partner

violence. Capture-recapture is a technique that is multi-methodological and is

45

appropriately used when there are multiple incomplete registries of a certain
phenomenon. This research will ﬁrst test the sensitivity of the formula by using a
simulation study. Second, it will use three incomplete lists of victimized women: shelter,
Outreach, criminal justice (including police, prosecutor and hospital). The lists are
considered incomplete because the lists are not exhaustive based on the fact not all
persons who are victims of intimate partner violence report their case, nor do these
persons only report to a single agency. The lists of cases of women who are victims of
intimate partner violence from at least three agencies will have identiﬁers which will
allow the “linking” of cases from one database to the other. The links and nonlinks will
be entered into the contingency tables as mentioned above to determine the missing cell.
The ratio of linked cases to the second sample is estimated to be equal to the ratio of the
ﬁrst sample to the whole population. Point estimates will be calculated and followed up
with tests for validity, reliability and controlled for necessary assumptions when
appropriate.

In sum, capture-recapture provides a means to estimate the population of victims
of physical abuse. While there are some precautions to be used for this technique in
controlling for assumption violation, it is still a better means of estimation than using
survey research or registries of cases of intimate partner violence as capture-recapture is
better than any other existing enumeration measure (LaPorte, 1996). Characterizing the
population of victims needs to be established and capture-recapture is the best available

technique.

46

CHAPTER 3 — SIMULATIONS

I. Introduction

As a renewed interest in using capture-recapture methodology has arisen, so has
concurrent polarization of the literature into believers and skeptics (Hay, 1997). One
camp claims this provocative technique could be the cure-all to statistical, demographic,
and epidemiological pitfalls in population estimation because it does not encumber the
biases or costs of traditional techniques, such as surveys or registration systems (LaPorte,
1994; Watts et al., 1995; Shaw et al., 1996; Stephen, 1996). In contrast, there is growing
concern ﬁom another camp with validity issues of capture-recapture methods (Hay,
1997). This dialectic was the impetus for developing controls for violations of 'necessary
assumptions,’ (Fienberg, 1998); however, the debate has since reached a stalemate (Hay,
1997). Even with improvements to the methodology, the accuracy of the capture-
recapture is believed impossible to ascertain because it is used to estimate elusive and
invisible populations, which are unknown in the ﬁrst place (Hay, 1997). This chapter
will shed some light on the capture-recapture controversy by illustrating the logistics of
using capture-recapture, demonstrating the sensitivity of the model, and determining the
precision of capture-recapture methods in predicting the size of an already known
population.

This study overcomes research limitations by employing controlled experiments
in the form of simulations. It allows the population to be preset and the prediction
capabilities tested. In addition to testing the estimation power of the capture-recapture

method, this research generates a "normal" capture-recapture distribution. In sum, this

47

research allows the capture-recapture dialectic to transcend some of the barriers and to

move the discussion forward.

11. The Logistics of Capture-Recapture

Before demonstrating the precision and sensitivity of the capture-recapture model,
it is necessary to understand the logistics of the model. Therefore, the following example
will illustrate exactly how to employ this technique using three hypothetical data sources
in a population of 1000 women. There are 26 cases of victims of domestic violence with
ﬁctitious names for demonstration purposes for three databases (see Table 3.1). One of
these databases as a sole predictor of domestic violence (direct estimation procedure)
would create an estimate of 26 per thousand cases. It is evident that single registries of a
given phenomenon are missing other true cases and therefore, estimating incidence at the
rate of 26 per thousand would be an underestimate. The more “hidden” the population is,
the greater the underestimate becomes.

Similarly, the three databases cannot be simply added together to derive an
estimate of incidence which would yield a rate of 78 per thousand (see Table 1). This is
not correct because many of the cases are found in more than one registry.

Seemingly, the most logical way to derive an estimate of incidence would be to
add the three databases together and to subtract out cases which have been counted more
than once. This would yield a rate of 50 per thousand and is still a direct method of
estimation. It is assumed that none of these databases contain all true cases in the

population of interest, therefore, they are added together.

48

In this example as in real case registries, the three databases are not an exhaustive
collection of domestic violence cases. Capture-recapture can be employed because it
capitalizes on having more than one database and indirectly estimates the true population
of cases by measuring the “overlap” between databases and not the joining of databases.

Using the formula for three factor capture recapture, we indirectly estimate the
population by looking at the number of cases found in each database exclusive of the
other databases, the number of cases found jointly in all three databases, and the number
of cases found in a combination of two out of the three databases. Using
Capture/Recapture we derive an estimate of 68 cases of domestic violence per 1000
persons. Following suit, we estimate the standard error (not based on probability) to be
8.8. This could be used to create a conﬁdence interval of 58.8 to 76.4 cases of domestic
violence.

In sum, counting entire populations and sampling are sometimes inappropriate
research alternatives to estimating population size and even more so for hidden and

elusive populations.

49

Table 3.1 Hypothetical Samples

 

 

 

 

 

 

 

 

Sample 1 Sample 2 Sample 3
ID No. Name ID No. Name ID No. Name
1 Mary Albert 1 Mary Albert 2 Christine Bosco
2 Christine Bosco 3 Beatrice Carrey 26 Thelma Xavier
3 Beatrice Carrey 7 Dalia Gallagher 24 Kiadra Zolton
4 Gertrude Dalton 8 Loren Hall 4 Gertrude Dalton
5 Abigale Evans 11 Wanda Kirk 9 Vivian Ithica
6 Shantelle Figaro 12 Noreen Lavender 13 Fergie Mason
7 Dalia Gallagher 15 Ophelia Oswald 17 Yolanda Queens
8 Loren Hall 16 Halle Pierson 18 Patricia Radcliffe
9 Vivian Ithica 21 Quintena Upstein 1 Mary Albert
10 Eva Juno 25 Megan Yeltzen 3 Beatrice Carrey
ll Wanda Kirk 27 Andrea Apple 7 Dalia Gallagher
12 Noreen Lavender 28 Barbara Busch 8 Loren Hall
13 Fergie Mason 29 Cherry Coldwater 11 Wanda Kirk
l4 Xandria Nelson 30 Dorothy Dunn 27 Andrea Apple
15 Ophelia Oswald 31 Evelyn Edgar 28 Barbara Busch
16 Halle Pierson 32 Frani Fredrick 29 Cherry Coldwater
17 Yolanda Queens 33 Gail Getze 30 Dorothy Dunn
18 Patricia Radcliffe 34 Hedi Hopper 31 Evelyn Edgar
19 Indigo Sundry 35 Josephine Jaguar 43 Sheila Saber
20 Zena Tandy 36 Kyla Kola 44 Terri Treefold
21 Quintena Upstein 37 Luanna Larrow 45 Wilma Wallace
22 Justine Verigo 38 Margaret Mead 46 Ariel Arson
23 Ursula Watson 39 Natasha Nixon 47 Bethany Bardell
24 Kiadra Zolton 40 Orlanda Opal 48 Chloe Clemens
25 Megan Yeltzen 41 Paula Paddington 49 Diedra Dunson
26 Thelma Xavier 42 Rachel Ripzeld 50 Yvette Youth

 

111. Effects of Database Sensitivity to Model

A Simulation of the capture-recapture formula will demonstrate how sensitive the

model is to the data. For trials 1 through 12, we set the total population at 1000. In this

simulation, the uni-sample, bi-sample and tri-sample probabilities of being captured are

varied to determine how sensitive the formula is to capture. In this example, the

probability of being captured in sample one, two, or three is written as Pl , P2, and P3

50

respectively. The probability of being captured in sample one (P1) is the probability one

person out of a thousand is in section A, B, D, or E.

For trial 1: the probability of being captured in sample one is P = .33. The same is true
for samples two and three (see Table 3.2). The probability of being captured in the
intersection of samples one and two (see section B and E in Figure 3.2) given the person
has already been captured in sample one or two is set at P12/1 and P12/2 = .30
respectively. The same probability is set for P23 and P13. Finally, the probability for
being captured in all three databases (P123) given the person has already been captured in
Samples 1 AND 2, Samples 1 AND 3, and Samples 1 AND 2 is set at .33. Given these
uni-sample, bi-sample and tri-sample probabilities, the estimate of the total population5

is 1242.

 

5 This simulation is not intended to estimate realistic population sizes because dependencies have NOT
been controlled, rather this exercise is a demonstration of the sensitivity of the model to dependencies.

51

Figure 3.1 Sections of Probability

For trials 2-4: The probabilities of the uni-sample and the tri-samples remain constant at
P=.33 while the bi-sample probabilities are decreased by .5 per subsequent trial (See

Table 3.2). With each decrease, the population estimate increases dramatically.

For trials 5-8: The uni-sample and the bi-sample probabilities are held constant at .33
and the tri-sample probability is decreased by .5 per subsequent trial. In contrast to trials
1-4, the decreasing probability has the opposite effect of decreasing the population

estimates (See Table 3.2)

For Trials 9-12: The bi-sample and tri-sample probabilities are held constant at .33 and

the uni-sample probabilities are decreased by .5 per subsequent trial. This decrease in

probability also has a negative effect on the population estimates (see Table 3.2)

52

In sum, the model is sensitive to the probability of being captured. Also, the dramatic
increases and decreases in the intersections of the three samples are indicative of the
importance of matching cases. For example, if there is one case located in the intersection
of samples one, two and three (Section E in Figure 3.1), and only two out of the three
sources are matched, then it would have an incremental effect on the population estimate
as opposed to a negative effect. This would lead to a decrease in the population estimate
as we see in Table 3.2, the more like a person is to be captured in the two sample
probability, the smaller the population estimate. An error such as this would have a
double effect since the case would increase the bi-sample probability as well as decrease
the tri-sample probability. The capture-recapture formula is more sensitive to errors for

estimating populations than traditional survey research statistics.

Table 3.2 Probabilities of Beirg Captured

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Trial P1 P2 P3 PlZ/l P12/2 P13/1 P13/3 P23/2 P23/3 P123/I P123/2 P1233 estimate
1 0.33 0.33 0.33 0.30 0.30 0.30 0.30 0.30 0.30 0.33 0.33 0.33 1242
2 0.33 0.33 0.33 0.25 0.25 0.25 0.25 0.25 0.25 0.33 0.33 0.33 1949
3 0.33 0.33 0.33 0.20 0.20 0.20 0.20 0.20 0.20 0.33 0.33 0.33 3564
4 0.33 0.33 0.33 0.15 0.15 0.15 0.15 0.15 0.15 0.33 0.33 0.33 7819
5 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.30 0.30 0.30 920
6 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.25 0.25 0.25 826
7 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.20 0.20 0.20 764
8 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.15 0.15 0.15 723
9 0.3 0.3 0.3 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 909
10 0.25 0.25 0.25 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 758
11 0.2 0.2 0.2 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 606
12 0.15 0.15 0.15 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 455

 

 

VI. Yes, but does it really work?
Given the logistics and sensitivity of capture-recapture, it is still not possible to

determine the efficacy of the technique for indirectly estimating the population size. This

53

technique is used when the true size of the population is unknown, therefore, ascertaining
the accuracy is difﬁcult. As discussed in the reliability and validity discussions in the
research methods chapter of this dissertation, there are signiﬁcant beneﬁts of having
multiple samples from which to estimate the same population as is the case in capture-

recapture. However, there are other means to determine precision.

A. Empirical Reality
There is signiﬁcant evidence in previous research studies that capture-recapture

netted good estimates of invisible populations. For example, public health workers in
Bangkok suspected much higher rates of heroin use than were detected in survey data and
registries. Higher rates were suspected because public health researchers were able to
determine the percentage of heroin users who were HIV positive. The number of HIV
cases increased more than the reported number of heroin users. In an epidemiological
study using capture-recapture Mastro et al. (1994) estimated the number of injection drug
users in Bangkok. Mastro et al. (1994) was able to count those cases missed by direct
estimation procedures. An additional six thousand heroin users were identiﬁed which
directly reﬂected the increase in HIV cases that were known to be contracted from heroin

usage.

B. Other Applications
Animal scientists6 have long since monitored animal and insect species using

capture-recapture. With this technique wildlife specialists have learned how many

 

‘ The US Fish and Wildlife Services, the National Wildlife Federation, and the Biological Resources
Division of the US Geological Survey

54

animals within a species exist, sex ratios, location, migratory patterns, frequency of
breeding, habitat ecology, survival rates and fertility rates. The information these
scientists collect regarding animal species is so intrinsically speciﬁc that several species
on the verge of extinction have been rescued due to the tailored “Recover Programs”.
“Animal demographers” understand the fertility, mortality, migration processes and
population size of some elusive creatures (Boukhout, 1994; Schemnitz, 1980, Seber,

1993)

C. The Precision of the Capture-Recapture technique

In reality we can never determine if a capture-recapture population estimate is
accurate, but in theory we can. A simulation can elucidate the precision with which
capture-recapture is able to estimate the population.

In the following example, a two-factor model of capture-recapture is used to
predict a preset population of 1000 and 2000. A hundred trials were calculated for each
level of probability at the given preset population size. The Simulation calculated
estimates of the population according to each probability of capture. The average
estimate and standard deviation of the 100 trials are listed in Table 3.3. As the probability
of being captured increases, the mean estimate is closer to the real population and the
smaller the standard deviation becomes. This simulation was only calculated for two
factor models as there are no dependencies. The three factor model can only
accommodate speciﬁc dependencies between samples and therefore, an estimate for

comparison is not possible without log-linear modeling.

55

When the number of cases captured in the samples drops below 15%, the standard

deviation becomes quite large. AS the probability increases for capture, the smaller the

standard deviation becomes. The inverse relationship between probability of capture and

standard deviation is consistent regardless of sample size. However, since standard

deviation is a function of sample size the statistic “Coefﬁcient of Variability” is also

calculated. The Coefﬁcient of Variability takes into account the fact that distributions

with very large means usually have larger standard deviations by dividing the standard

deviation by the mean (Blalock, 1960). In the ﬁnal column of Table 3.3, the Coefﬁcient

dramatically decreases when the probability of capture is less than .15.

Table 3.3 Measure of Precision

 

 

Probability Coefﬁcient
Sample of Mean Maximum Minimum Standard of

Size Cyture7 Estimate Estimate Estimate Deviation Variability
1000 .05 1298 3105 302 721 .56
1000 .10 l 124 2179 602 294 .26
1000 .15 1029 1527 656 192 .18
1000 .20 1027 1349 791 124 .12
1000 .25 1025 1386 889 88 .08
1000 .30 1012 1262 891 77 .07
2000 .05 2524 10494 993 1489 .58
2000 .10 2056 3534 1259 458 .22
2000 .15 2046 3071 1577 269 .13
2000 .20 2024 2817 1648 199 .09
2000 .25 1996 2451 1658 137 .07
2000 .30 1992 2263 1767 98 .05

 

 

 

 

 

 

 

D. Distribution of Capture-Recapture Estimates

In another type of simulation, a typical distribution of capture-recapture estimates

is created. Using a simulation program to randomly generate capture-recapture estimates,

 

7 Probability is Pm and Pm

56

two-hundred trials were executed. The two-factor capture-recapture model generated a
mean score of 1036 with bi-sample probabilities P12/l and P12/2 of .15. These estimates
create a distribution that is skewed to the right. The skew of the capture-recapture

distribution is 1.09 as shown in Figure 3.2.

Figure 3.2 Distribution of Capture-Recapture Estimates

STIMATE

 

 

 

  

in.

5'

: “.m-IIIQII
3 run run
5 . III-Ill

 

"I‘a'a‘tu’o’o‘o’o’mﬁ‘h‘b
"I'.

IMTE

V. Conclusions

In response to the ﬁrst research question, can the capture-recapture technique
indirectly estimate the size of an invisible population, capture-recapture is a useful
statistical technique to estimate the size of invisible populations; however, there are some
cautionary measures to be implemented during application. This technique must be
employed with strict scientiﬁc rigor by utilizing methodologies to control for violations
of the necessary assumptions. These simulations have demonstrated that the model is

indeed sensitive and therefore, it would not sufﬁce to just give point estimates as opposed

57

to conﬁdence intervals. This simulation has deﬁned some parameters for estimating the
population. As shown in Table 3.3, when sample representation drops below 15%, the
conﬁdence placed in the estimate is reduced considerably as the standard deviation
doubles. When sample representation of the observed cases exceeds 15%, the standard
deviation decreases substantially and the range of estimates decreases. The smaller the
probability of being captured in the sample, the less conﬁdence the researcher should
hold in the point estimate and rely more heavily on the conﬁdence intervals constructed
around the point estimate.

The capture-recapture estimates indicate a positively skewed distribution. This
distribution should be considered when calculating standard errors for use in conﬁdence
intervals. The upper parameters should have more credence than the lower parameters
because of the positive skew. This study supports F ienberg’s (1998) contention that it is
best to proﬁle population estimates with intervals to reduce the errors and the interval
between the point estimate and the upper parameter are more likely to contain the true
population than the lower parameter.

In sum, capture-recapture can be a powerful technique in population enumeration
as long as the researcher has an overall understanding of model sensitivity and point

estimates.

58

CHAPTER 4 — CAPTURE-RECAPTURE

1. Subject and Database Descriptions

The data to be used for these analyses come from multiple sources in Marquette
County between January 1995 and July 1997. There are three analytic sources which “is a
list which may be constructed from one or more original sources” (Hook and Regal 1995,
p. 244). The three sources are: l. Prosecutor’s database; 2. Domestic Violence Shelter
ﬁles; 3. Outreach Services ﬁles (see ﬁgure 4.18). The original sources, “a particular list of
cases from some institution” (Hook and Regal 1995, p. 244) have been collapsed into the

analytic sources.

Figure 4.1 Analytic Sources for Capture-Recapture

 

 

' Cases from each agency list may also be represented in one or both of the other agencies as duplicated
cases are not subtracted out.

59

Both estimations of incidence and prevalence will be calculated based on these
data. Incidence is the total number of physical assaults by an intimate partner within the
given time frame. Whereas, prevalence is the number of victims physically assaulted by
an intimate partner within the give time frame. Some victims may have experienced
multiple incidents of physical violence, however, prevalence is an indicator of the
proportion of the population affected as opposed to the frequency.

Cases of intimate partner violence enter the prosecutor’s database via the medical
system and the policing agencies or independent complainants of Marquette County.
According to Michigan Law, policing agencies must formally report all calls, reports, or
investigations to the prosecutor’s ofﬁce within two days, also known as the 48-hour
report.9 Not all persons in the prosecutor’s database have been arrested but all cases have
been authorized to go to trial based on evidence. Suspects are frequently prosecuted
without having been arrested in cases of intimate partner violence. Hershel and
Hutchinson (1993) reported that in more than 50% of the cases of intimate partner
violence, an arrest is not made because the suspect is not present when the officer arrives.
Maxwell (1998) stated in these cases, the perpetrator can be arraigned without ever
having been arrested. The Marquette prosecutor’s office receives cases of intimate

partner violence from the following police agencies:

I Forsyth Township Police Department
I Republic Township Police Department

 

’ x. SB 587 - P.A. 63 OF 1994. Effective 7-1-94.

Amends the Code of Criminal Procedure to require police ofﬁcers to make a written report, including
standard basic information, in response to all domestic violence calls, requires that such reports are
submitted to the prosecutors ofﬁce for review. Also revises the domestic violence victims rights notice to
include information about the police response and clearer direction toward victim rights and referrals.
Repeals the statue that formerly required the court to dismiss a case without prosecutor's consent if the
victim stated s/he had received civil satisfaction.

60

Marquette County Sheriff 3 Department
Ishpeming Township Police Department
Negaunee Police Department

Richmond Township Police Department
Northern Michigan University Public Safety
Marquette Police Department

Michigan State Police

Ishpeming Police Department

Chocolay Township Police Department

Medical personnel are also required to report10 all persons presenting at their
agency with injuries sustained from intimate partner altercations to the appropriate police
department. In turn, those cases are forwarded by the police department to the
prosecutor’s ofﬁce in the 48-hour report. The two hospitals in Marquette County are
Marquette General and Bell Memorial in the towns of Marquette and Ishpeming
respectively. Both these hospitals reside in Marquette County.

All cases of male on male (22) and female on female (23) assaults were removed
from the prosecutor’s database because the other data sources did not contain same sex
assaults during the research time period and therefore, analysis was not possible without
overlapping cases. Male-on-female and female-on-male violence were analyzed

separately.

 

'0 It is the duty of every person or corporation conducting or managing any hospital, pharmacy, or ward in
this state, to which any person(s) suffering from any wound or other injury inﬂicted by means of a knife,
gun, pistol or other deadly weapon, or by other means of violence shall come, to report the same
immediately. The report should be both by telephone and in writing to the Chief of Police or Sheriff of the
village, city or county in which the hospital or pharmacy is located. The report must state the name and the
residence of the person, if known, his whereabouts, and the character and extent of the injuries. It is also the
duty of every physician or surgeon who has any person suffering from any wound or injury inﬂicted in the
manner above mentioned under his care to make a similar report to the appropriate officers named above.
Any person, ﬁrm or corporation violating any provision of the section is guilty of a misdemeanor. MCLA
750.411.

61

II. Male-on-Female Intimate Partner Violence

The prosecutor’s database contained 184 females during this two and half year
study. The number of incidents (198) was greater than the number of victims as some
victims experience multiple attacks from their perpetrator and thus, a victim may have
more than one case referred to the prosecutor’s ofﬁce.

There are two Outreach Offices run by the Women’s Center Inc. of Marquette
County. Their services are similar to the programs found in the shelter, however, they
differ in that they are for women who are not in need of shelter. Outreach services
include crisis counseling and support, housing assistance, childcare, legal advocacy, and
transportation to legal assistance. There were 280 women using the Outreach services
during the two and a half-year study period. These women reported 472 incidents of
domestic violence to either the Ishpeming ofﬁce or the Marquette office.

Finally, Harbor House is the sole domestic violence shelter for victims of intimate
partner violence in Marquette County. There were 136 women seeking shelter on 155
occasions within the two and a half-year study period. This agency also provided shelter
for their children. Children are recognized victims of intimate partner violence as they are
traumatized by their mother’s abuse in addition to the fact that batterers are 45-5 9% more
likely to be child abusers (Jones, 1994; Edleson and Tolman, 1992). However, for
purposes of this study, children are excluded from analysis. The shelter performs many of
the same services as the Outreach ofﬁce except they also offer safe accommodations for

women and children in hiding from their perpetrator.

62

III. Necessary Assumptions
There are four assumptions that must be met in order to utilize the capture-
recapture technique as described by Nanan and White, (1997) Hook and Regal, (1995)

and Fienberg, (1998).

A. Closure

The population under study is closed. The population of Marquette County
remains stable in demographic terms during the two and a half-year period. One
consideration is the number of IPV related homicides where the victim is no longer “at
risk” for assaults. There were two domestic homicides during the period of study. This
mortality will not have an effect on the prevalence rate, but it may have affected the
incidence rate although the number is so small it would have had negligible effects on the
estimations.

Closure of population is more crucial in animal ecology studies where the samples
are taken sequentially. In the case of this research, data were being recorded
simultaneously in all sources. This is less problematic because even if a victim moved out
of the area, she still had the potential to be captured in the three sources during her
tenure. Finally, closure of population is a form of dependency and can be controlled for

as is discussed further down.

B. Perfect matching
Individuals identiﬁed in one source are perfectly matched in another without error

with no mismatches or non-matches. There is a lower risk of matching error, as the

63

investigator is extremely familiar with the population and the victims. F urtherrnore, a
single investigator read and entered the data into the databases for both the outreach and
the shelter. In addition, there were several case ‘identiﬁers’ such as victim ﬁrst name, last
name, middle name, maiden name, age, birthdate, race, address, perpetrator last name,
ﬁrst name, date of incident. The prosecutor’s database also recorded the outcome of the
case, which provided further information for identifying cases. The shelters and outreach
ofﬁces both maintained records on victims and their outcomes, changes of names, birth
of children, moves, etc. Therefore, it was possible to check matches by misspelled names,
naming variations, nicknames, and changed names.

Data were also sorted by perpetrator and victim birthdates, to further check for
potential matches. The victim’s date of birth was requested in both the prosecutor and
shelter sources, whereas, the Outreach ofﬁces used self-reported “age” of victim. There
appeared to be some discrepancy between age generated from the “date of incident”
minus the “date of birth” and the self reported age for some women over the age of forty.
After careful rechecking of the records from the original source, it was concluded that
some women presenting in the Outreach office were misreporting their age. Occasionally,
a respondent would misreport her age and in those cases, the older the respondent, the
greater number of years would be subtracted from actual age. Subtracting years was only
found in women age of forty-three and older. The age of victim was missing in 52 of the
cases, however, there were enough other identiﬁers to determine positive matches. The
cases were matched on several ﬁelds creating conﬁdence in the matching. The age

generated from the prosecutor source was extended to the reported age of the respondent

64

in the event of a discrepancy because prosecutor date of birth was obtained from ofﬁcial

records such as a driver’s license.

C. Independence

The independence assrunption is that the probability of being in one list is not
affected by the probability of being on another. This assumption is violated in the case of
intimate partner violence for Marquette County. As communities strive to combat
intimate partner violence, agencies are collaborating more with each other in an attempt
to have a coordinated response to domestic violence. Women presenting in shelters and
outreach ofﬁces are encouraged to have their injuries treated by medical personnel and
report their cases to the police. Similarly, police ofﬁcers that respond to a domestic are
mandated to provide the victim with information on the shelter and outreach ofﬁce.
Furthermore, there is a community council in Marquette County created to implement a
coordinated agency response and to improve services for victims. All Marquette
hospitals, police agencies, women’s services, and prosecutors are active participants in
the council. There are several domestic violence projects located in Marquette County
that improve the services and increase communications between the agencies. Two of the
major projects are ‘The Justice Project’ implemented by the prosecutor’s ofﬁce and
funded by the National Institute of Justice and the Marquette Research for Justice and
Violence Agencies (MR JAVA) funded by the Michigan Department of Community
Health. In addition, there are several other smaller domestic violence projects which are
funded by the Family Independence Agency and Victims Compensation Board that

contribute to dependencies of data sources.

65

Dependencies can be thought of as both positive and negative and both can be
present within the same model. In the case of Marquette County, while we expect there to
be a positive relationship between the shelter/outreach and the hospital or the
Shelter/outreach and the police department, we also expect there to be a negative
relationship between the police department and the shelter. The rationale for this
assumption is based on the logic that with improved police response there is a decreased
need for shelter. If the perpetrator is removed by arrest and jail time, a woman is not in
need of hiding. Similarly, the Outreach Programs and the shelter provide many of the
same services except Outreach does not provide shelter. Therefore, if a victim uses the
services of a shelter, she will not need Outreach Services. However, if a woman is
frequenting an Outreach ofﬁce and her safety becomes compromised, she will be referred
to the shelter. Many women in shelter are not trusting of the criminal justice system and
do not want to report to the police department for fear of an increased retaliation by the
perpetrator and perception the legal process will prolong the connection of the perpetrator
to the victim (Personal communication with shelter director May 1998).

In sum, there are several theoretical positive and negative dependencies in this
research model. It would appear these data should support a model with two-way
interactions between all the sources. Fienberg (1972) made considerable contributions to
the capture-recapture estimation technique with his use of log-linear modeling to control
for sample dependency, which will be employed in this research and discussed later in
this chapter. Capture-Recapture estimates are based on Maximum Likelihood Estimates

of parameters of log-linear modeling (Haberrnan, 1974). Proofs of these estimates are

66

based on the existence and uniqueness of Maximum Likelihood Estimates in exponential

family distributions (Andersen, 1974).

D. Homogeneity

The ﬁnal assumption to be met is homogeneity (also known as catchability) -
whereby all subjects must have an equal probability of being captured. The degree of
homogeneity can bias the results by both overestimating and underestimating the
population (Hook and Regal, 1995; Nanan and White, 1997). Variable catchability is also
a form of source dependency that can be reduced through log-linear models. In addition,
this assumption can be met by stratifying the sample according to certain characteristics
to look for differential estimations. An indicator of variable catchability is to explore if
any population characteristics differ between the different sources. One data source may
be more sensitive to a certain characteristic and therefore, may be more likely to catch a
person based on a particular characteristic. An analysis of socio-demographic
characteristics revealed that 79.2% of the sources were White, 3.5% were Black, 3.5%
were Asian, 11.7% were American Indian, 1.7% were Hispanic, and .4% were mixed
descendent. The racial distribution of the general population of Marquette County is
Black 1.7%, American Indian 1.3%, Asian .8%, and Hispanic .8%. There was slight over
representation of Blacks in the three data sources and underrepresentation of Hispanics.
There was an extreme overrepresentation of Asians in the three data sources. A chi
square test of race and data source netted a value of 5.39 with p < .864 indicating there
was no signiﬁcant difference between race and source of data. However, there are still

differences between victims and the general population.

67

The average age for the combined sources was 33.1 years with a standard
deviation of 10.8. The average age of clients in the Shelter data was 35.6 years, 34.3
years for the Outreach source and 30.0 years for the Prosecutor source. A one-way
ANOVA resulted in an F value of 12.98 with a p < .000 indicating there was variability
of age between datasources and there was a Signiﬁcant difference between the average
ages of each data source. The median age for the general population of Marquette County
is 30.7 years. This test should be considered cautiously as it is not an absolute that the
varying characteristics between sources are indicative of variable catchability, only that
the average age is signiﬁcantly different between data sources. However, as hypothesized
in this research, there is indication younger women are more likely to be found in
institutional data than older women and therefore, more likely to be caught in any one
data source.

Each institutional database provides a separate snapshot of domestic violence.
This amounts to three pictures from different perspectives of a single phenomenon.
Individually, a single source can give a unique perspective of the situation but is not able
to stand alone as an indicator of IPV. Analogously, these three sources are ﬁnding the
same racial composition among the three institutional sources, however, they are not
ﬁnding the same age composition which MAY indicate there are characteristics of the
institution itself that lends itself to “catching” a speciﬁc age group more easily. These
data will be tested for varying catchability by stratifying older and younger aged women
into independent estimates of IPV. These data will be stratiﬁed aﬁer identifying the best

ﬁtting model.

68

IV. Maximum Likelihood Estimator (MLE)
After subtracting out the duplication between the three data sources, there are 520
women and 825 incidents of intimate partner violence in this study. The overlap of the

incidence and prevalence studies is demonstrated in ﬁgures 4.2 and 4.3 respectively.

Figure 4.2 Overlap of Incidence Data Sources

prosecutor

 

69

Figure 4.3 Overlap of Prevalence Data Sources

 
 

grosecutor

  
  

  

mm 3 211

Outreach

 

The three data sources are divided into sections of overlapping cases and non-overlapping

cases (Table 4.1).

Table 4.1 Sections and Intersections of 3 Sources

 

Nobs = Observed cases mm + mm + “1122 + In211+ mm + 111212 + mm
N1 = Prosecutor Source mm + mm + mm + mm

N2= Shelter Source mm + mm + mm + mm

N3 = Outreach source m1” + m2“ '1' 111221 + m121

N = Total Population mm + Nob,

mm = Invisible Pgulation See Maximum Likelihood Estimator’s Below

 

Databases with known “intersections” lend themselves well to capture-recapture to

estimate the invisible population and multiple sources lend themselves well to log-linear

70

modeling (Fienberg, 1972). Using the traditional Peterson estimation (1896) or Lincoln
index (1930) we assume our samples are independent for two-source capture-recapture.

Under the condition of independence (taken from Fienberg, 1972) we know that:

mil mlz =
ml: m21

1

The cross-product ratio for the expected entries in the 2 X 2 table is unity. Thus, the

maximum likelihood estimate of mg; allows us to estimate the missing cell by:

mlz ”121
mu

22

Therefore, to estimate the total population N, the missing cell, m2; is estimated by the

cross-product ratio and added to the observed population, Nob}, which is calculated by:

Nob: = m12+m21+mll

Therefore:

m m
N = 452—24 + (rn12+m21+ml 1)
ll

71

V. Log-linear Modeling to Control for Sample Dependency

By ﬁtting three or more data sources to contingency tables as in Figure 4.4, we

can estimate N.

Figure 4.4 Contingency Table for Three Sources

 

 

 

 

 

PROSECUTOR
present absent
SHELTER SHELTER
present absent present absent
OUTREACH present mm mm ”1211 "1221
absent "1112 mm "1212 "1222

 

 

 

 

 

 

 

The odds ratio is set for level one of source 1 equal to that for level two (Fienberg, 1998).

mlilm221 = m112m222
m121m211 mm ”1212

We solve to estimate mm .'

_ mlll m122 mm m221
m222 ‘—
m112m121m211

And thus can estimate:

N = Nobs+m222

Where the observed population is:

72

Nob: : mlll + m221+ m121+ m211+ m122 + m212 + mllZ

As in the case of this study, three data sources will be used to estimate the
invisible population. There are eight potential models that may ﬁt the data derived from
three sources based on the interdependencies (Hook and Regal, 1995). “AS with
independence in 2-way case, we can’t test for appropriateness of no 2"d-order interaction
assumption, but we can ﬁt other log-linear models to the data” (F ienberg, 1998). To test

for 2“‘1 order interactions, there must be four or more sources of data.

Where:

108 maj, = u + um) + u2(,, + 713(k) + 1112(1)) + “13(ik)+ 112301;)

Where:

u = The Constant

u 1 (,j = The Main Effect of Source 1 (prosecutor data)
u 20) = The Main Effect of Source 2 (shelter data)

u 30:) = The Main Effect of Source 3 (outreach data)
mm) = The Interaction Effect of Source 1 and 2

u 13m.) = The Interaction Effect of Source 1 and 3
11230-1.) = The Interaction Effect of Source 2 and 3

The following eight models are listed by Hook and Regal (1995) as the potential

models for three-source capture-recapture log linear control.

73

Table 4.2 Interactions Accordingto Model

 

 

 

 

degrees of

Interactions Model freedom
Independence 1 3
Interactions between databases 1 and 2 2 2
Interactions between databases 1 and 3 3 2
Interactions between databases 2 and 3 4 2
Interactions between databases 1 and 2 and databases 1 and 3 5 l
Interactions between databases 1 and 2 and databases 2 and 3 6 1
Interactions between databases 2 and 3 and databases 1 and 3 7 l
Interactions between databases 1 and 2 and databases 1 and 3 and 8 0
databases 2 and 3 (saturated model)

 

The corresponding Maximum likelihood estimates (see below) of m 222 using the

alternative models to control for sample dependency are as follows (see ﬁgure 4.4 for cell

labels):

Model 1:
Model 2:
Model 3:
Model 4:
Model 5:
Model 6:
Model 7:
Model 8:

"1222 = N - Nob:

"1222 = ("1112 + "2122 +m212)(m221)/(m111 + mm + mm)
"1222 = ("1112 + "1122 +m221)(m212)/(m111 + "1112 + "1211)
"1222 = (mm + "1221 +m212)(m122)/(m111 + mm + "1112)
M222 = (m212m221)/ "1211

"1222 = (m212ml22)/ "1112

"1222 = (m122m221)/m121

"1222 = ("1111 "1122 M221 mzlz)/( "112101112 "1211)

VI. Establishing Incidence and Prevalence

For these analyses the three data sources were ﬁtted to each of the eight models to

derive an estimate for the missing cell m 222. Their corresponding Maximum Likelihood

Estimates (MLE) are listed below in Table 4.3 for both prevalence and incidence.

Prevalence refers to the number of battered women and incidence refers to the number of

incidents of intimate partner violence.

74

Table 4.3 Incidence and Prevalence MLE by Model

 

 

 

 

 

 

 

Model Incidence MLE Incidence GI Prevalence MLE Prevalence G2

2 1,413 257.975 734 173.6 f
3 901 226.0 * 545 157.4 *
4 3,030 58.5 * 1,796 28.2 *
5 770 205.6 * 388 148.2 *
6 3,990 38.1 * 3,139 19.0 *
7 3,510 6.2 ° 1,817 2.8
8 11,910 1.0 5,853 .008

t p < .000

°p<05

In addition to using three sources in the log linear models, there are three
additional models whereby, one of the data sources is dropped for a two-source restricted
model (Hook and Regal, 1995). The Maximum Likelihood Estimates are as follows in

Table 4.4 for both incidence and prevalence for comparative purposes.

Table 4.4 Two-source Restricted Models for Three Data Sources

 

 

 

Model Formula Incidence Prevalence
Source 1 verses 2 (N,)(N2)/(m1 1 l + mm) 2,790 2,275
(Prosecutor and Shelter)
Source 1 verses 3 (N1)(N3)/(m, 11 + mm) 3,594 2,061
(Prosecutor and Outreach)
Source 2 verses 3 (N2)(N3)/(mm + m2, 1) 1,306 747
(Shelter and Outreach)

 

 

 

The wide range of estimates is indicative of both negative and positive
dependencies in the data sources (Hook and Regal, 1995) as was suspected in this case.

This indicates there is no three way positive or negative dependency in this model. A

75

three-way positive dependency would mean that being present in one data source would
increase the likelihood of a person presenting in both the other two data sources.
Similarly, a three-way negative dependency would mean that being present in one data
source reduces the likelihood a person appears in the other two data sources. Unmodeled
positive dependencies tend to underestimate the size of total population and unmodeled
negative dependence tends to overestimate size of total population (Hook and Regal,
1995). Now that multiple models were used to estimate the MLE, we must determine
which model is the “best ﬁt” for the data. Theoretically, we begin with the simple models
devoid of dependencies and add in parameters until the model is saturated. Due to the
cross-over of agency referrals, we expect there to be dependencies between data sources.
The dependencies are shown ranging from a single two source dependency (model 2) to a
model (8) where all two sample interactions are controlled. Theoretically, the simple
models do not ﬁt the data because of the known dependencies. Further tests of statistical
signiﬁcance of these models determine the simplest model with sufﬁcient parameters to
ﬁt the data. Using SPSS, these data were analyzed by selecting the saturated model and
using the process of backward elimination to test the various models. The Iterative
Proportional Fit algorithm converged at iteration 1, meaning the saturated model is the
best ﬁt for the incidence data. There was nothing signiﬁcantly added to the model by
dropping any of the parameters. The likelihood-ratio goodness-of-ﬁt statistic (G2)ll for
the saturated model equals 0 and is insigniﬁcant. The likelihood-ratio goodness-of-ﬁt

statistic (Demaris, 1992) is calculated by:

 

” The model which generates the lowest G2 value while being insigniﬁcant is the model with the best ﬁt.

76

C}2 = 221,]. log ﬂ”—

‘1

Therefore, the log-linear model:

108mg], = u + u...) + ”2(1) + um) + 1112(1)) + 111301;) + u23uk)

is the best ﬁtting model for the incidence data and therefore, we accept the estimate
derived with model 8 (see Table 4.2) as our estimate for incidents of intimate partner
violence in Marquette County. Thus by knowing mm = 11,910, we can solve for N, the
predicted population, by adding the missing cell to the observed population. Hence,

N = 11,910 + 739 = 12,649
In sum, based on these data there were an estimated 12,649 incidents of intimate partner
violence in Marquette County between January 1995 and July 1997. However, due to the
difﬁculty in deﬁning an incident12 and problems with clustering, the incidence values are
not expected to be accurate as the prevalence estimates.

The prevalence data were also tested using log-linear modeling to determine
which model is the best ﬁt. The model selected by the backward elimination process as
the best ﬁt was model 7 (See Table 4.2), which dropped the parameter of the interaction
between the prosecutor and the shelter sources. The likelihood ratio for model seven was
2.8 and was signiﬁcant at p< .246. Model seven is the most simple while being

insigniﬁcant and therefore, is accepted as the best ﬁt. Therefore, this log-linear model

 

‘2 Some women reported beatings that lasted for extended periods of time with intervals of rest for their
assailant or multiple beatings within a single day. Furthermore, it was impossible to determine which
arrests correlated with a speciﬁc incidence since they may have occurred on different days. Prevalence
estimates are not problematic as they only require matching the victim between samples.

77

best describes the data in a simpler model with one less parameter by setting this

parameter, U12(ik) , equal to zero:
log mat = u + “110+ ”20) + "300 + "1201+ uncle) + “23010

We know that the estimate generated by model seven is 1,817. Therefore, adding the

observed cases to the unobserved cases we can solve for N.

N = 520 +1,817 = 2337

Based on these data there were an estimated 2,337 women in Marquette County between
January 1995 and July 1997 who experienced one or more assaults by an intimate

partner.

VII. Stratifying the Data

The data are stratiﬁed according to age group: Those women less than forty years
of age at the time of their assault and those women aged forty years and older. The
division of age into two groups is based on the assumption that most women have
completed fertility by their 40th year. Using the best model for the prevalence estimations,

the following estimations in Table 4.5 are generated according to age group.

78

Table 4.5 Prevalence Estimations Stratiﬁed by ﬁe

 

 

Datal3 Total Population” Women < 40 Women 40 +
m”) 7 5 2
mm 153 127 26
"112] 16 13 3
m1]; 4 4 0
M21] 39 24 15
"1212 85 56 29
"1221 116 82 34
mm l 10915 801 295
N1 180 149 31
N2 135 89 46
N3 178 124 54
Nob, 420 311 109

 

 

 

 

These sections and intersections were used to estimate the prevalence according to age-

group in Table 4.6 using the best ﬁt model (model #7) as stated above.

Table 4.6 Prevalence Estimates According to Ag

 

 

Agggroup (”1122721220071”) "2222 Nob: ML C/R Ascertainment
Total 153 X 116/ 16 1109 420 1529 .37
Women<40 127x82/13 801 311 1112 .38
Women 40 & > 26 x 34 / 3 295 109 440 .37

 

 

 

 

 

 

As found in Table 4.6, the data sources are divided into younger and older age

groups. However, the unstratiﬁed data fall short of the independent estimations sources

by 23 cases, meaning the sum of the prevalence population estimates (N) for younger and

older women (1112 and 440 respectively) is greater (1552) than the prevalence

population estimate in the unstratiﬁed model (1 5 29). We would expect a different pattern

 

'3 See Figures 4.3 and 4.4 for notation explanation of Table 4.5.
“ These estimates include those for both age groups. However, these estimates will deviate from the total
population estimates stated above because there were 107 cases used in the previous estimations that did
not include age of victim and therefore, those cases are deleted from the age-stratiﬁed estimations.

79

of estimates if there existed varying catchability according to age. Since the sum of the
Maximum Likelihood Estimates of the stratiﬁed samples approximates the unstratiﬁed
sample, it would appear that there is not variable catchability. One of the age groups
should predict a much higher estimate or a much lower estimate if there were sufﬁcient
variability. Therefore, the age effects on catchability do not create under and over
estimates. This is consistent with the ﬁndings of Gondolf, Chang, and Laporte (1997) of a
batterer’s program where they used reports by victims, police, and perpetrators to
estimate the incidence of re-assault after perpetrators of domestic violence were made to
attend a batterer’s prevention program. Gondolf et al. (1997) did not ﬁnd varying
catchability due to demographic characteristics and relationship to perpetrator. However,
there appeared to be some bias in the sampling by catching the more severe cases of
assault, as is expected in this analysis“. Those persons presenting in emergency rooms,
police departments, and shelters are generally going to be the more severe cases that
result in injuries. Using the unstratiﬁed model is sufﬁcient for this study, however, it will
net a conservative estimate as this study focuses on the physical assaults that lead to
injury.

In the Capture-Recapture Ascertainment Column of Table 4.6 there is evidence
that this estimation technique varies slightly by estimating the prevalence according to
age group. This is evident from dividing the observed population of the three data sources
by the predicted population prevalence. We ﬁnd that 37% of the predicted population is

explained by the observed population for both the unstratiﬁed model and the stratiﬁed

 

'5 This estimate is NOT a sum of the two age subgroups, but rather an independent estimation based on cell
counts.

1“This does not necessarily indicate that the estimate will exclude the less severe cases of violence because
those cases can be included in the invisible cell.

80

model for the older age-group while the younger age-group’s observed population
explains 38% of the predicted population estimate. Meaning, there were slightly more
observed cases used to predict the invisible cases for older women than younger women.
In sum, it would appear that older women are indeed an invisible population, however,

not more invisible than younger women.

VIII. Calculating Standard Error for Capture-Recapture Models

The standard error can be used to create a type of conﬁdence interval; however,
since it is not a true interval based on probability, it can create an incorrect lower limit
which is a false-positive, therefore, an interval should not be used or used with caution.
There is a better technique based on goodness of ﬁt to determine whether a point estimate
is appropriate (Hook et al., 1995).

For a saturated model that assumes all two-way interactions between sources and
no second order interaction for a three source model, the asymptotic variance “for this
estimate for N is intimately related to the asymptotic variance of a log-linear contrast”

(Fienberg, 1998). The asymptotic variance is written as:

l l
+

”ILL/c3 mm

 

 

V(N)=m:22 (2 )

It can be problematic to use the asymptotic variance of a saturated model as often
the interval length will have a lower estimate than the actual observed cases. This is
especially the case when the sample size is not that large (Hook and Regal, 1995).

Fortunately, the prevalence data ﬁt Model number 7 (see table 4.2) and therefore, the

81

asymptotic variance can be calculated by using the expected frequencies instead of the
observed frequencies. Therefore, the asymptotic variance derived from the log-linear
model speciﬁed by setting exactly one 2-factor term equal to zero (taken from F ienberg,

1972) “1207!) , = 0,

I 1 1 I
V (N ) = m:22( + + +
m122 m212 mm mm

 

 

 

In a larger sample, the standard error would be small enough to create a

meaningful conﬁdence interval, however, in this case, the sample size is too small.

IX. Point Estimates for Capture-Recapture

As seen in Table 4.7 below, many of the estimates fall within a close range. There
are some point estimates generated by some models that fall too low because the model
has not controlled for a speciﬁc dependency. For example, when looking at the data
intersections in ﬁgure 4.3, we can see that the largest dependency is between the Shelter
data and the outreach data (sources 2 and 3). Therefore, we expect an estimation that does
not control for this dependency to completely underestimate the population size. Hence,
in the two source model for sources 2 vs. 3 generates a point estimate below the best
model point estimate because the model does not incorporate dependencies between
those two data sources. Another example of a gross undercount is in the case of model
ﬁve that controls for all two-way interactions minus the interaction between source 2 and
source 3. Analogously, model three is a good estimator since it does incorporate the

dependencies between sources two and three. Model 7 is a better estimator because it also

82

adds in the effect between the prosecutor’s data and the outreach data and makes an
additional correction for the dependency between source 1 and 3. In sum, these range of
estimates validate our best model Maximum Likelihood Estimate because they land
theoretically, where they should. When using the asymptotic variance to create a
conﬁdence interval, often the interval is quite wide as is evident in this case. As Cormack
points out, the right parameter should be regarded as a correct upper conﬁdence level,
while the left parameter should be regarded with caution because the capture - recapture
prediction distribution is skewed to the right and therefore, we expect there to be a bias
with the left parameter. Fienberg (1998) has recommended using proﬁling of intervals as
a means for reducing the conﬁdence interval and to eliminate the possibility of a left
parameter that is less than the actual observed cases. For purposes of this research, this
point estimate is a good indicator of the prevalence of victims of intimate partner

violence and is within expected limits.

Table 4.7 Estimated Number of Women by Model

 

 

(a) (‘0) Sum
(a+b)
Number of Estimated
Samples Model Observed cases Prevalence MLE Prevalence
3 2 520 734 1,254
3 3 520 545 1,065
3 4 520 1,796 2,316
3 5 520 388 908
3 6 520 3,139 3,659
3 7 520 1,817 2,337
3 8 520 5,853 6,373
2 1 vs. 2 320 2,275 2,595
2 1 vs. 3 464 2,061 2,525
2 2vs.3 416 747 1,163

 

 

 

 

 

83

X. Female-on-Male Violence

The prosecutor’s database contained 45 reported women who assaulted men. The
domestic violence shelter reported zero cases of men seeking shelter from women and the
outreach had two males claiming to have been assaulted by females. Using the two
source restricted model (see Table 4.4) there is an estimated prevalence of 137 male
victims over the course of two years and seven months.

These estimates of female-on-male violence should be regarded with extreme caution for
several reasons. First, the intersection between the prosecutor’s database and the outreach
database only contained one case. This is an extremely small sample and overlap with
which to make reliable estimates.

Second, there are only two sources on which the estimations are based.
Controlling for dependencies in this model is impossible and it is likely that the
assumption of independence is violated.

Third, there is some question as to the validity of these being real cases of female
perpetuated violence against males. The majority of these cases are from the prosecutor’s
database which come from police reports. Due to the new arrest laws, police ofﬁcers have
more authority to arrest perpetrators of Intimate Partner Violence (IPV).l7 In fact, police

ofﬁcers are encouraged to arrest perpetrators with fewer criteria. '8 This creates a bias in

 

'7 ARREST WITHOUT A WARRANT; ASSAULT AND BATTERY OR INFLICTION OF SERIOUS
INJURY WITHIN HOUSEHOLD [MCLA 764. 15a (1980)].

This law is commonly known as the domestic violence warrantiess arrest statute. It allows the police ofﬁcer
to make an arrest if the ofﬁcer has "reasonable cause" to believe that an assault has taken place, or is taking
place, and that the person who committed the violation is a spouse, former spouse, or a person who resides
or who has resided in the same household as the victim, or has a child in common with the victim. Under
these circumstances, the ofﬁcer may arrest the suspect without a warrant, whether the violation was
committed in the presence of the officer or not.

'8 S. HB 4360 - PA. 69 of 1994. Effective 7-1-94. Amends the Code of Criminal Procedure by requiring
police agencies to establish written policies regarding their response to domestic violence by January 1,
1995. Policy requirements include an emphasis on arrest as the preferred response upon a ﬁnding of

84

the system as ﬁ'equently women who have been victimized by intimate partner violence
are arrested for physically defending themselves or reacting physically to a perceived
threat of physical violence (Browne, 1987). Hamberger (1990) found that after the
institution of domestic violence mandating arrest laws — women were found to be
arrested at a twelve fold increase while men’s rates of arrest only doubled.

Thirteen out of 45 (29%) of the female-on-male cases in this study were
dismissed by the judge due to insufﬁcient evidence or were not proven guilty beyond a
reasonable doubt. In contrast only 20% of the male-on-female assaults were dismissed
due to insufﬁcient evidence or failure to prove guilt. Upon further analysis it was found
that 33% women charged with domestic assault/assault and battery in court had histories
of being battered by the same male. In one of the cases, the police arrested both the
woman and the man for ﬁghting. Twenty percent (9) of these women had been beaten on
multiple occasions by this same male. The most extreme case is a woman who sought
shelter or contacted the police ten times within the time period of this study. Eight of
these women have been in the same court previously with the same partner, only the man
was the suspect in the previous cases. None of these women in this study had received a
jail sentence as a result of assaulting a male while 23% of the men received a jail
sentence. Three percent of the male victims were treated at the hospital for injuries while

twice as many women were treated.

 

probable cause that a crime was committed in a domestic situation. Provisions for insuring victim safety
and assistance are also required.

85

XI. Conclusions

In this chapter research questions three and four are addressed Does older couple
violence compare to younger couple? In this analysis we found that there are
signiﬁcantly fewer cases of abuse among older couples than among younger couples
(1102 verses 404). However, there are signiﬁcantly fewer older women at risk meaning
there are fewer older women involved in an intimate relationship. The American trend of
females marrying older males along with longer life expectancies of women, has left
more older women single in their later years than younger women (State Demographer,
1997)

In these analyses, it is apparent that although fewer older women are being
battered, they do not appear to be more elusive and invisible than younger women. The
total population estimate of older women is explained by 37% of the observed
population. For younger women, the percentage is only minimally higher (3 8%).

The fourth research question, “Are women as likely to perpetuate violence as men? ” is
clearly answered. Based on these analyses it appears that men are more than 17 times as
likely to physically assault their intimate partner. While there is evidence some females
do perpetrate violence against males, it is not clear the contextual setting for that
violence. In the qualitative analyses of these cases, there appears to be signiﬁcant
evidence that a large proportion of the female-on-male violence cases may be victims of
domestic violence acting in self-defense. Furthermore, the changes in the criminal laws
make it necessary for police to arrest all perpetrators of physical violence - - even if she is

female and regardless of the context of the violence.

86

In sum, the statistical technique capture-recapture is able to estimate the
prevalence of intimate partner violence for Marquette County. Based on the data from the
prosecutor’s ofﬁce, the domestic violence shelter, and the outreach services, there were
only 520 documented incidents of male perpetrated violence against a female intimate
partner over the course of two years and seven months. Based on the capture recapture
indirect estimates of domestic violence, it is more likely that the actual number of number
of victims is closer to 2,337. This suggests that the ofﬁcial case records only account for
approximately twenty-two percent of the total number of victims and 6.5% of the

incidents.

87

CHAPTER 5 — COMPARATIVE STUDIES OF INTIMATE PARTNER VIOLENCE

I. Introduction

This dissertation has established that intimate partner violence has several
methodological issues to overcome in estimating incidence and prevalence. In addition to
measuring the frequency, there are other outstanding challenges to this ﬁeld. Intimate
partner violence estimation also involves deﬁning what constitutes violence and who are
its victims. These parameters are as varied as the researchers that approach the issue. This
chapter will discuss differences between two national surveys and a recent statewide
study in Michigan. This study will also demonstrate how the methodologies lead to
varying results as well as limitations. Finally, the results of the surveys will be compared

with estimates from the capture-recapture study described in the preceding chapter.

11. Survey Studies
A. Michigan Violence Against Women Study

In 1996, the Michigan Department of Community Health and Health Research
Associates, in conjunction with the Centers for Disease Control and Prevention and the
Gallup Organization, developed a survey to improve the knowledge of the prevalence and
characteristics of violence. This study was modeled after the ﬁrst national survey on
violence against women in Canada (Statistics Canada, 1993). There were 1848 women
interviewed for the Gallup study on violence. The overall response rate was 51.8% and
the refusal rate was 17.2%. The sample was analyzed using SUDAAN statistics software

to control for sampling effect.

88

1. Sample

The sample was obtained from random digit dialing and one woman was
randomly selected once the household contact was initiated. Respondents were limited to
women between the ages of 18 and 69. The data were weighted to represent the overall

Michigan population.

2. Marital Status

This study includes all single, married, divorced, and never married women.

3. Deﬁnition

The respondents were asked regarding violent behaviors so that women would
report “violent acts” that they may not normally have reported as violence. For example,
instead of asking women if they were involved with a batterer, they would query whether
certain acts occurred to them. Violence was deﬁned as any threats, objects thrown at
victim, pushed, grabbed, shoved, Slapped, kicked, bit, hit, choked, beaten, used weapon,

and forced sexual activity.

4. Gender

The focus of this study was violence against women, therefore, no males were

interviewed.

89

5. Rates

There were 3.2% of the women in the Violence Against Women Study for
Michigan who reported being physically assaulted by their intimate partner in the past
year. That rate increases to 4.8% when we only consider the percentage of women
involved in an intimate relationship or at risk as opposed to the general population of
women. This rate of violence experienced by a current partner is less than half the
proportion of the population that Straus and Gelles found in their survey, the National
Family Violence Survey, but nearly three times as high as the rates found in the National

Crime Victimization Survey.

B. The National Crime Victim’s Survey
The Bureau of Justice Statistics commissioned the ongoing survey the National

Crime Victimization Survey. This survey began in 1972 and has continued to the present.

1. Sample

This sample was designed using stratiﬁed, multistage cluster sampling. After a
housing unit was selected, every resident from that unit was interviewed by the US
Census. All persons age twelve and older were included in the survey. This survey
generated a response rate of 96%. This study contained 101,000 persons from 50,000

housing units.

90

2. Marital Status

This study includes all persons for single, married, divorced, and never married

persons.

3. Deﬁnition
Violence was deﬁned as any attack or threat with a weapon such as a bat, pan,
scissors, stick; thrown item such as rock or bottle; grabbing, punching, choking, rape,

attempted rape or other sexual attack, and face to face threats.

4. Gender
Based on the revised National Victimization Survey, the rate for female victims

was more than Six times higher than the rate for male victims.

5. Rates
This survey created rates of intimate partner violence as 9.3 per 1000 for females
and 1.4 for males. This rate is less than a tenth of the estimates found in the National

Survey of Family Violence.

C. The National Family Violence Survey
The National Institute of Mental Health sponsored the National Family Violence
Survey conducted in 1976 and again in 1985. The primary investigators of both of these

studies were Murray Straus from the University of New Hampshire and Richard Gelles

91

from the University of Rhode Island. The response rate for this survey was 84%

(Johnson, 1995).

I . Sample

The survey comes from a national random sample of 6,002 persons.

2. Marital Status
This survey was limited to persons who were married or cohabiting at the time of

the study.

3. Definition
Violence was deﬁned as, “an act carried out with the intention or perceived

intention of physically hurting another person ” (Gelles and Straus, 1990).

4. Gender
Based on both waves of the National F amily Violence Survey, Straus and Gelles

9

suggest that women perpetrate violence against men1 more than men perpetrate violence

against women. They found evidence of this in both mild and severe forms of violence.

5. Rates
This survey sets the proportion of couples experiencing violence at 11% and 12%

perpetrated by males and females respectively for currently married or co-habitating.

 

'9 Although women reported slightly higher rates of perpetration than men, these differences were
insigniﬁcant.

92

III. Comparative Estimates from Capture-Recapture

1. Sample

The capture-recapture analysis is based on three institutional data sources from
Marquette County, Michigan for 1995-1997. Those data sources include authorized cases
of violence perpetrated by an intimate partner of the Marquette County Prosecutor’s
office, records of women who stayed in the domestic violence Shelter, and battered

women who sought counseling services.

2. Marital Status

This analysis included all persons single, married, separated, and divorced.

3. Definition

Violence was deﬁned as any physical assault.

4. Gender

Both males and females were considered for this study as long as they were
victimized by a person of the opposite sex. Based on the capture-recapture analyses it
appears that men are more than 17 times as likely to physically assault their intimate
partner than females. This is the same sex disparity found in Kincaid’s (1982) study of

court ﬁles in Ontario, Canada.

93

5. Rates

The prevalence estimates generated from the capture-recapture analysis in the
preceding chapter sets the annual intimate partner violence rate at 4.7% for female
victims aged 18-69. This proportion is not directly comparable with those persons
surveyed in the Michigan study, the National Crime Victim Survey or the National
Family Violence Survey because those rates are only based on varying age groups and
marital status. However, for comparison purposes Table 5.1 loosely demonstrates the
varying rates. If we only look at women who are “at risk” for abuse, the number of
women with an intimate partner is used as the denominator to calculate a “mate-rate”.
The Michigan Violence Against Women survey derived the rate for women with intimate
partners at 68% for the state of Michigan. Using this proportion of the population of
women aged 18-69, the number of women in relationships who were assaulted at least
once within the year is 17%. This proportion is higher than Straus and Gelles found in

their two national surveys by approximately 5-6%.

Table 5.1 Survey Estimates

 

 

 

 

 

 

 

 

 

Victim
Annual
Survey Prevalence Parameters
Michigan Violence Against Women 3.2% All women
4.8% Women involved in relationship
National Crime Victim Survey 0.93% All women
National Family Violence Survey 11.0% All currently married or cohabiting
women
Capture-Recapture 4.7% All women
17.0% Women involved in relationship

 

94

IV. Methodological Limitations and Variances
The varying results of the intimate partner violence studies are a ﬁmction of
methodological differences as well as limitations. Methodological choices can serve to

deﬂate and inﬂate estimates of intimate partner violence.

A. Intimate Partner Status

If only married and co-habitating women are studied as victims of intimate
partner violence, a signiﬁcant portion of the population is excluded. Rosenberg (1991)
found “Married women are the least likely, and single, separated, and divorced women
the most likely, to experience assault by a male intimate” (page 135). The National Crime
Survey data Show that separated women experience much higher rates of violence. In
fact, the period when women are separating ﬁom their male partners is the most
dangerous time of a relationship (Browne, 1987) . Jones (1994) found the time period
when women separate from their male partner is when most homicides occur. Rosenberg
(1991) reports that 16% of women presenting for medical assistance due to intimate
partner violence are married, whereas 55 percent of assaults among separated women are
perpetrated by a male intimate. Excluding respondents who are not currently involved in
a domestic relationship or who have terminated an intimate relationship eliminates a large
proportion of the violent population. Bachman and Saltzman (1995) found that rates of
intimate partner violence for separated women are more than eight times as high as those

for married women.

95

B. Survey research

Survey research precludes respondents who are severely victimized and isolated
by their abuser from participating in the survey. Sample bias is a reality for all
researchers; however, for intimate partner violence researchers the problem is
confounded by the very nature of being a battered woman. First, if it were possible to
interview battered women in representative surveys, there is substantial evidence that
victims as well as perpetrators do not disclose violence (Johnson, 1995). Researchers
have found that women report being abused more than their assailant reported abusing
her (White and Koss, 1991; Stets and Henderson; 1991; DeKeseredy and Kelly (1993).
Finally, the same characteristics of being a battered woman would also prevent her from
being included in a random sample. Survey respondents and nonrespondents can differ
signiﬁcantly. The dynamics of battering include extreme isolation and fear of reporting
(Pence, 1996) which has been systematically reported in multiple studies. “Men who
systematically terrorize their wives would hardly be likely to agree to participate in such
a survey, and the women whom they beat would probably be terrified at the possibility
that their husband might ﬁnd out they had answered such questions” (Johnson, 1995).
Some of the tactics used by abusers (Pence, 1996) that would prevent victims from

participating in a survey include:

I locking her in the home.

I calling her frequently during the day to make sure she is there and to make sure
she is not on the phone.

I Threatening her with death if she leaves.

I Keeping her at home by not leaving her with a car or clocking the mileage on the
car to prevent car usage.

96

Johnson (1995) found that in the National Family Violence Survey there were
only a handful of women who reported abuse similar to the rate of women in shelters.
After extrapolating this proportion of women to the population, he found the number of
cases with severe levels of violence identical to shelter clients was far below the known
number of women using shelters (Johnson, 1995). Battered women are not represented in
national surveys. The very nature of the abuse prevents the victim ﬁ'om participating.
Kirkwood (1993) reported victims having suffered so many blows, both physically and
psychologically, they felt their assaults too trivial to report to an interviewer. Other
victims reported not wanting to discuss such painful memories with a researcher (Smith,

1987).

C. Gender symmetry/asymmetry

Research conducted by Straus and Gelles (1990) indicates that women assault
men slightly more than men assault women”. The Conﬂict Tactic Scales borne of the
Family Violence Survey do NOT take into consideration the acts of violence it purports
to measure. As multiple researchers point out, these results do not reﬂect the social reality
because the survey instrument was designed in a manner that did not discern who
initiated the violence, the size and strength of the persons involved, and the nature of the
relationship21 (Dobash, Dobash, Wilson, and Daly, 1992; Saunders, 1986; Adams
Jackson, and Lauby, 1988; Berk, Loseke, Berk, and Rauma, 1983; Fields and Kirchner,

1978; Pleck, Pleck, Grossman, and Bart, 1978; Wardell, Gillespie and Lefﬂer, 1983).

 

2° These differences were found to be insigniﬁcant, Straus concluded that men and women batter each other
equally as much.

97

The Conﬂict Tactic Scales have been utilized in other studies that qualiﬁed the violence
perpetrated by women. When women were asked to estimate the frequency of their
violence to prevent themselves from immediate harm, there was indication a signiﬁcant
portion of these women were indeed acting in self-defense (DeKeseredy et a], 1997;
Saunders, 1986).

In the National Crime Victimization Surveys 1992-1996 and the 1994 Study of
Injured Victims of Violence, three out of four female victims of domestic violence
reported defending themselves during an assault (US Department of Justice, 1998). The
implications of the Family Violence Survey of female initiated violence contrast
dramatically with clinical studies of Shelters and police departments, as well as those
from another national survey (Dobash and Dobash, 1992; Martin, 1981; Kincaid, 1982).
Gauquin (1978) found that 97% of the assaults were by males in the ﬁrst National Crime
Survey. Bachman and Saltzman (1995) found that women are more likely to be killed
from husbands, boyfriends, and ex-partners than men.

For the Marquette study described in Chapter 4, further analysis reveals many of
those women who were reportedly perpetrators of intimate partner violence have been
victims of battering and further, those men who were recorded as victims have also been
perpetrators of violence in previous occasions. This additional information gives doubt as
to the legitimacy of many of those cases by providing a contextual background.
Furthermore, in only one of those cases was it clear that the female had superior strength
and a physical advantage over the male within the two years and seven months of this

study.

 

2' There are other signiﬁcant methodological problems outside the realm of this study with the Conﬂict
Tactic’s Scale as it attempts to provide some hierarchical model for various forms of violence based on a

98

D. Agency Studies

Studies conducted in hospitals, shelters and police departments are subject to
serious clinical fallacy. Some of the reasons victims of intimate partner violence do not
report to the police is they consider the incident a private or personal matter, they are
afraid their perpetrator will retaliate, or they feel the police will not do anything (Bureau
of Justice Statistics, 1998). Using clinical data as estimators for incidence excludes a
large proportion of the cases.

Furthermore, studying characteristics of domestic violence on only those persons
found in clinical samples cannot be generalized to the whole population. There may be
signiﬁcant differences from women in domestic violence Shelters from women who were
unsuccessful at leaving their abuser from women who were successful at leaving their
abuser without the help of social service agencies. However, as long as some of those
women are captured in those clinical data, then the technique of capture-recapture can

estimate those women missing.

E. Pretense of Study

The Family Violence Survey was posed to respondents as a study regarding
family violence and tactics couples employ to resolve conﬂict. The Michigan Study was
posed as a study of several categories of violence perpetrated against women. In contrast,
the National Crime Victimization Survey approaches potential respondents as a general
study of crime. Many victims of domestic violence still do not see this brand of violence

as a crime (V AWNET, 1998). This may explain part of the varying rates.

 

preconceived danger potential.

99

F. Respondents

The National Crime Victimization Survey interviews all members of the selected
household. Victims may be reluctant to disclose assaults they experienced by members of
the same household. The victims may also be uncomfortable reporting events that are in
conﬂict with the reports of their assailant. Both the Michigan study and the Family
Violence Survey only interviewed one person from the household which may have left
the victims more open to disclosure and may also explain part of the discrepancy in the

estimates.

G. Age Parameters

The Michigan Study did not include women younger than 18 or older than 65.
This would act as an inﬂating factor because persons in the highest risk age groups are
those persons 19-29 (Bachman and Salzrnan, 1995). The Michigan study includes that
age group but excludes those women who are in known lower risk groups. The National
Crime Victimization Survey includes persons in the 12-18 group and 65 + group which
will deﬂate the rates of violence. Women are more likely to be widowed and single and
the least likely to experience domestic violence and they are included in this survey

(VAWNET, 1998).
H. Bounding

The Michigan Study and the National Family Violence Survey are not

longitudinal studies such as the National Crime Victimization Study. Respondents are

100

asked in all three studies to recollect over the past year incidents of violence. In the ﬁrst
two studies, the victim may very well misremember events that happened within the
speciﬁed time frame. Respondents may report an event that occurred before the time
period of interest. In contrast, the National Crime Victimization Survey is given on a six
month basis and when victims report an incident, it is check against their previous record
and respondents are queried whether the stated incident is indeed a new event or one that
was mentioned in the previous wave. Bounding prevents respondents from including
incidents from outside the time period of interest. Studies have shown unbounded

interviews tend to overproduce estimates of incidents (Bachman and Taylor, 1994).

V. Conclusions

In sum, measuring violence perpetrated by an intimate partner or ex-partner will
always be a methodological challenge. DeKeseredy and Schwartz (1996) reported it was
impossible to obtain totally accurate data and that some methods were more reliable than
others. Given their conceptual ﬁamework, they were correct to think that the “best
procedures are representative sample self-report and victimization surveys specifically
designed to collect data on male-to-female violence” (page 330). DeKeseredy and
Schwartz made recommendations to increase the validity and reliability of survey
research as they knew institutional records were gross undercounts. Nonetheless, capture-
recapture remains a viable option to overcome many of these sampling issues in
estimating woman battering frequency.

In response to the second research question, ‘are there significantly more cases of

domestic violence than are reported or estimated from surveys? ’ The estimates from

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capture-recapture are higher than the Michigan Violence Against Women Study, the
National Crime Victim’s Survey, and the National F arnily Violence Survey. Survey
research is known to exclude victims of intimate partner violence as well as police or
shelter registries. Capture-recapture can estimate the proportion of persons missing from
both research strategies and empirically demonstrated, there is a large number of victims

missing from traditional estimation procedures.

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CHAPTER 6 -— CONCLUSION

1. Summary of Dissertation
A. Theoretical Lull

This dissertation employs new research methods to study violence and to open up
the theoretical development in a ﬂedgling ﬁeld with stagnate theoretical progress.
Sociologists, along with psychologists and criminologist largely ignored woman battering
until the seventies. The Journal of Marriage and the Family, one of the most prestigious
and highly read journals for sociologists, has been in existence for 60 years. Not a single
article discussed intimate partner violence for the ﬁrst 30 years (O’Brien, 1971).
Sociologists only broached the topic of wife abuse as recently as the 70’s. Primarily
those researchers were "family sociologists" who were in the process of exchanging the
traditional functionalism as a research framework for conﬂict theory. Family violence
sociologists are a product of the early 1970’s Civil Rights and Vietnam War era and have
not developed their theoretical frameworks much beyond those of the early days.

Although Straus (1973) has subscribed to General Systems Theory and Gelles
(1983) supports Exchange and Social Control Theory, these two theories are based on the
same family violence framework. Both place violence in the family system and conﬂict.
The former theoretical framework implies that violence is a universal part of a family
system and that the system itself regulates the levels of violence. The latter framework
suggests violence is used as a means to gain something unless there are signiﬁcant costs.
While both these theories supply separate etiologies for the use of violence, both these

theories normalize violence by assuming violence is a normative reaction - - either as a

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response to conﬂict or as a means to gaining something from the partner. When Straus
(1973) proclaimed the "marriage license is a hitting license" he was merely trying to
emphasize the pervasiveness of spouse abuse. However, implicit in this statement is the
belief violence is a normal tactic with full family participation.

The family violence theorists have failed for the past three decades to explain the
disparity between social reality and their research ﬁndings. Furthermore, violence is a
complex issue where all forms cannot be understood within a single framework,
regardless if that framework has developed into a meta-theoretical level as Gelles has
suggested (1995). The etiology of fathers raping their daughters differs signiﬁcantly from
men battering women or adult children abusing elder parents. These various forms of
family violence must be desegregated to be understood. It is even probable that there is
more than one distinct form of women battering (Johnson, 1995). Theoretical
development for family violence must occur independently.

F arnily violence theorists acknowledge sexism and patriarchy as a signiﬁcant
factor in partner abuse, but still violence is conceptualized from the family structure
where it is plausible either partner initiates the violence as a normal response to everyday
conﬂicts or as a means to gain power over a partner. Feminist researchers are better able
to explain intimate partner violence as rooted in the patriarchal structure but have only
recently begun to consider various motivations and types of woman battering. A
univariate explanation of woman battering does not explain some of the signiﬁcant
ﬁndings of other researchers. The feminist perspective provides the best explanation for

battered women even though it requires further development.

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B. Theoretical Impasse

This dissertation takes a novel methodological approach to intimate partner
violence to test existing theoretical frameworks and resolve the feminist/family impasse.
The results of this dissertation ﬁnd supporting evidence for the feminist ﬁamework Since
the inception of violence research, advocates for battered women and their research
counterparts, feminist theorists, have been at odds with the family sociologists. The
irreconcilable difference is rooted in the tenet of family violence theorists that women
assault men equally as much as men batter women and that violence is a normal, albeit
unacceptable, part of married life. Ultimately, family theorists ﬁnd support for these
allegations in their research while feminist theorists ﬁnd contradictory evidence. In fact,
feminist researchers ﬁnd very little if any evidence that women assault men, except under
the auspices of self-defense. This dissertation could resolve some of the polarization of

subscribers of the family violence theory and the feminist theory.

C. Methods Suspend Theoretical Development and Testing

The methodology used in this dissertation is a new medium to study woman
battering to lead to theoretical development. Family violence sociologists have theorized
based on two national surveys (Straus and Gelles, 1973; 1985) while feminist researchers
primarily have collected their data ﬁom clinical trials. There are exceptions where
feminist researchers use surveys and family violence researchers rely on clinical trials
(Johnson, 1995), but still these two divergent theorists stand by earlier holdings. The
national surveys do not yield ﬁndings consistent with the clinical trials conducted in

hospitals, police departments, courtrooms, and domestic violence shelters.

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Inherent in studies of woman battering are serious methodological barriers.
Survey researchers are not able to get an accurate depiction of woman battering because
their studies could not possibly be a representative portion of the population since victims
must be missing (Johnson, 1995). The very nature of intimate partner violence precludes
the victims from such activities as leaving their home, using a car, using the telephone,
and Spending time with other people (Pence, 1996). These activities are essential for
participants of survey research.

Similarly, clinical trials cannot describe victims who never seek help or report
their assailant. As feminist researchers acknowledge, the victimized population is mostly
undercounted (Y110 and Bograd, 1988). The sampling bias of non-representation and
clinical fallacy have left feminist researchers and family sociologists stunted in their
theoretical development. This dissertation has demonstrated a means to describe those
victims that never report battering as well as enumerating those women who are missing
from survey research. This dissertation has overcome these monumental research barriers
in woman battering research.

For Sociologists, social reality, methodology, and theory are closely tied to each
other. Methodology allows us to test our hypotheses to establish our theory creating an
intrinsic dependence. Theory establishes the demand put on the methods which “open
up” the theory. Sociologists theorize but are unable to critically examine theory with
limited methods. If there is theoretical development, the theories cannot be critically
examined with limited methodologies. This has been the case of the two major theoretical

frameworks used in domestic violence. This dissertation has methodologically pushed the

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general body of knowledge in the ﬁeld of violence research forward by overcoming the

methodological limitations of violence researchers.

D. Capture-Recapture

This dissertation has allowed for the victim population to be counted even when
victims did not report the assault to the police or a social service agency and when
victims were not represented in surveys regarding violence. The hidden population of
victims is counted using capture-recapture as well as those persons known to be battered.
These ﬁndings do not support the status quo, the family violence framework, even though
mainstream sociologists are the dominant, most accepted, and quoted ideology in the
ﬁeld of domestic violence research (Yllo, 1995). Their contentions of gender symmetry
in intimate partner violence is not supported. In contrast, the capture-recapture estimates
found it extremely rare for men to be assaulted by women. Further qualitative
investigation revealed that a signiﬁcant portion of the men who were assaulted by women
had frequently battered that same woman on previous occasions. Furthermore, some of
those “male victims” had severely and ﬁequently battered their female partners which
suggests those women may have been acting in self-defense or assaulted their male
partners unprovoked because of a perception of vulnerability (Browne, 1987).

Another ﬁnding from the capture—recapture estimates is the signiﬁcant number of
older battered women. This dissertation provides challenging results as to the age
structure of the victimized population. Generally, women victims are thought to be quite
young (Stark and F litcraft, 1991) when in fact, the average ages of victims from this

analysis and from case records suggest a much older population in the case of Marquette

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County. Stark and F litcraft (1991) suggest violence is more common among women
under the age of 30 while they did acknowledge older women were victimized as well.
Results from the data placed the average women who frequented shelters in her mid 30’s.
In addition, there were several cases of woman battering by an intimate partner for
women who were at the end of their lifespan. A signiﬁcant portion of the battered
women’s population is invisible increasing the difﬁculty to characterize that population.
While these results are not in contradiction to any theoretical speculations about age and
violence, it does give us a better proﬁle of the population.

This study has provided better point estimate of frequency of intimate partner
violence in terms of both prevalence and incidence. Although the capture-recapture rates
are not directly comparable to other state and national surveys as well as institutional
studies, it appears a much larger proportion of the population is being battered in a given
year than indicated in the Michigan Violence Against Women Survey, National Crime
Victim’s Survey, and the National Family Violence Survey.

Capture-recapture is a compelling estimation technique ﬁrst used by wildlife
researchers (Peterson, 1896; Lincoln, 1930), brieﬂy used and forgotten by demographers
(Sekar and Deming, 1949), borrowed by epidemiologists (Wittes and Sidel, 1968),
improved by statisticians (Fienberg, 1972: Bishop et al., 1975) and fortunately, employed
once again by demographers (N anan and White, 1997). The application of capture-
recapture is becoming a more common and acceptable means of indirect estimation.
Recently, there have been innovative applications of this technique. The US government
is using capture-recapture to control for undercounting in the US Census (N anan and

White, 1997). Epidemiologists are using capture-recapture to estimate the size of illegal

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and covert populations such as prostitutes (McKeganey et al., 1992), homeless persons
(Fisher et al., 1994), and heroin users (Squires et al., 1995; Barnes, 1995). NASA has
employed this technique to count the number of stars in the universe (Fienberg, 1998).
Currently, the British Society for Statistics has research underway to estimate the size of
the World Wide Web (F ienberg, 1998). Capture-recapture is being used in a creative
fashion to estimate some difﬁcult research areas.

This dissertation has employed simulations to test the capture-recapture technique
to determine the sensitivity, the precision and the distribution of the model. Controlled
experimental simulations were able to demonstrate how sensitive the model is to the
probability of being captured and the importance of matching the data. The sensitivity
decreases as the sample size and overlap increases. If there are errors in the intersections
of data identiﬁcation, the effects are doubled in the skewing of the results. These
simulations also show the effect of being captured in one or more samples while using
the capture-recapture technique.

Further simulations demonstrate capture-recapture the precision of the technique
in forming point estimates substantially increases when the observed cases represent
more than 15% of the estimated cases. When the ratio of observed to estimated cases
drops below the 15% mark, the conﬁdence interval grows substantially. Still, even with
the larger standard errors, proﬁling the intervals using a variety of techniques can give
the researcher a better notion of the true population size than by not using the capture-
recapture technique.

Some researchers have been reluctant to accept this indirect estimation procedure

as a valid and reliable technique (Hay, 1997). However, statistical controls and

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innovations of capture-recapture have assured this is a valid and reliable technique. There
have been several reﬁnements and varied means to control the violations of necessary
assumptions22 by some outstanding statisticians (Fienberg, 1972; Bishop et al., 1975;
Fienberg, 1998; Cormick, 1981; Ding, 1990; Ding and Fienberg, 1994; Sekar and
Deming, 1949; Alho, 1990; Alho et al., 1993; Erickson and Kadane, 1985; Darroch et al.,
1993; Agresti, 1994; Kelderman, 1984; Agresti and Lang, 1993; Biggieri et. al., 1997).
This technique has been victim of excessive criticism probably based in its unusual
origins and characteristics. That coupled with its deviation from traditional research
strategies has cast further doubt. The basic structure of the technique and the statistical
controls require a sophisticated and high level of statistical knowledge. These Simulations
demonstrate the ability of capture-recapture to estimate the size of a known population
with exceptional precision.

The simulations demonstrate this technique is a valid and reliable methodology
and also illustrate the need to meet the necessary assumptions. If those assumptions are
violated”, it is necessary to employ statistical controls and techniques. As long as a
researcher can successfully employ those techniques while using capture-recapture, the
method will be valid and reliable.

In sum, capture-recapture has successfully been used to estimate the prevalence of
intimate partner violence. This novel approach to intimate partner violence should shed
light on this complicated social problem and push the body of generalizable knowledge

ahead on who are the victims and the pervasiveness of the problem.

 

22 The majority of these techniques were either unnecessary or not applicable to the research at hand and
therefore, there is little discussion of these other controls. Several researchers are currently in the process of
reﬁning these statistical controls even further.

23 Researchers should assume this to always be the case.

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II. Signiﬁcance of Study
A. Paradigm Shift

Capture-recapture has held up as a feasible and viable option for estimating the
population of victims of intimate partner violence in this dissertation. It proved to be an
excellent means of estimating the size of the population when the registries of the shelter,
the outreach program, and the prosecutor’s ofﬁce were known to contain accurate but not
exhaustive cases. This study has provided violence researchers with a new paradigm for
estimating the size of the victimized populations previously thought impossible to count

(DeKeseredy and Schwartz, 1996).

B. Tests Existing Theories of Intimate Partner Violence

Until now, there has not been an alternative methodology to test the two major
theories of intimate partner violence and to a 25 year old theoretical impasse. This
dissertation lends support to the feminist framework for conceptualizing violence
between intimates with gender asymmetry and women being the major victims of
intimate partner violence. This dissertation also challenges the dominant theories of
intimate partner violence known as the family violence perspective. This study has
provided an additional approach to testing the theories of intimate partner violence while
rising above the barriers of clinical fallacy and non-representation. This study has
generated multiple estimates of intimate partner violence based on multiple samples

which lend support to the feminist perspective.

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C. Methods Have Provided Room for Theoretical Development

While this research has supported the feminist perspective, it has also enumerated
women who went undetected in previous clinical trials and surveys. While the feminist
perspective explains the scenario of women in shelters, police departments, court, and
emergency rooms, it does not necessarily explain the etiology of the violence of those
women who went undetected in previous studies. There is room for development within
the feminist perspective to explain other forms of violence against women.

Family violence sociologists need to re-examine their holdings that women are
battering men equally or even more than men batter women. Multiple studies, including
nationally representative surveys, clinical studies, as well as this capture-recapture study
ﬁnd no support for this tenet of the family violence theories. Given there are trace
examples of women assaulting men, the context of those injuries, the size disparity and
the intent of the assailant need to be considered.

Ultimately, even if there is a small minority of women assailing their male
partners, the proportion is not comparable and does not have the structural implications as
female battering. Intimate partner violence is analogous to racism. Behind an act of
discrimination by a white person comes with it the racial structural inequality of our
society because whites are politically in control and hold the reigns to the economy, the
workplace, the resources, and privilege. Even though it is possible to have reverse
discrimination based on prejudice against a white person by a minority, it is NOT
possible to have a person of color acting as a racist because that person is not in a societal

position of authority. Violence against women is similar. Even though women may act in

112

violence against their male partners, it is still the men who hold the political and
economic control and dominate women in a patriarchal structure where male privilege
prevails. “Woman battering” should be considered a patriarchal structural issue. Although
Steinmetz (1980) coined the term “husband-battering” and announced there was a hidden
social problem of violence against males, there is no evidence this occurs except in
isolated and rare events. To indicate otherwise, is a disservice to battered women and the
credibility of sociology. Many battered women’s advocates have gone so far as to accuse
the family violence sociologists of damaging the necessary support for battered women
by confounding these issues and digressing from the true social inequalities (Jones,

1994)

Reports of “husband battering” reach policy makers and are not always discerned
from substantiated research. Support for battered women is controlled by the legislature
who provide necessary funding to domestic violence shelters. In one example, a
Michigan senator in 1998 placed the funding of the Pontiac shelter in jeopardy. While
Shelters do provide safe housing and counseling for male victims in locations outside the
premises, this program was seen as discriminating. One man wanted to stay inside the
shelter with the other battered women and children (one of them being his wife) but was
referred to stay in another location. The funding that provided safety to hundreds of
women and children in one of the largest and busiest shelters in the state of Michigan was
at risk because of a perceived “battered husband”. Shelters were alerted their funding
would be jeopardized if battered men were refused entrance. The funding was not
revoked, however, false alarms take valuable time and resources best left devoted to

battered women. Researchers have a strong impact on policy makers who have the power

113

to help battered women and children. Researchers should focus their efforts on violence
against women instead of creating distracting “false alarms”. While it is appropriate to
consider all scenarios, substantiation requires replication.

The discipline of family sociology and their research methodologies should be
scrutinized carefully. Just as in the case of the family violence perspective, it is not
plausible to study complex family issues and to develop one theoretical framework with
which to explain all forms of violence. Family violence researchers are misguided in their
theoretical development and it is not clear if part of this problem is rooted in the overall

discipline as well.

D. Tests Precision and Sensitivity of Capture-Recapture

This dissertation has demonstrated that capture-recapture can be used with
conﬁdence to indirectly estimate the size of the population of battered women. However,
in addition, the simulations used in this dissertation also develop the understanding about
the technique itself by demonstrating how the technique holds up under various
conditions. The simulations also generate a distribution to provide researchers with an
understanding of the possible distribution of positively skewed estimates. Furthermore,
the simulations develop a pattern of standard deviations of population estimates based on

varying probabilities of being captured.
E. Future Applications

Capture-recapture can be used by sociologists for multiple purposes. First, the

technique is an excellent means to estimate the size of the population when clearly there

114

are incomplete data available from two or more sources. Second, capture-recapture can
be used to reﬁne estimations from survey research. Third, this technique could be used in
the evaluation of incomplete case ascertainment of registries and surveillance systems.
Capture-recapture would be an excellent technique to measure other invisible populations
that challenge social researchers such as sexual assault. The possibilities of this technique
to open up the theoretical development and to test existing theories are compelling. For
example, there is a twenty year debate between criminal justice theorists and feminist
psychological theorists regarding the prevalence of rape. The sexual assault prevalence
debate is even more heated than the family violence/ feminist gender
symmetry/asymmetry argument. Criminal Justice researcher’s response to the high levels
of sexual violence reported in national sexualviolence surveys have been received
poorly. Feminist researchers have been accused of research strategies that invent victims
of sexual assault (Gilbert, 1998). This technique could establish the pervasiveness of

sexual violence and provide an objective perspective.

F. Limitations
1. Cannot Positively Diﬁ'erentiate Violence Types

This methodology cannot distinguish different types of violence without
incorporating qualitative research methods. For example, Pillemer and Finkelhor describe
violence among the elderly as stemming from caretaker stress as well as intimate partner
violence that is comparable to younger couple violence. McLeer and Anwar (1989)
conducted a study on intentional injuries in the emergency room in Philadelphia. These

researchers noted there were several cases of teens who were mis-identiﬁed as cases of

115

child abuse and elders who were nus-identiﬁed as cases of elder abuse when in fact, they
received injuries from their intimate partners. This technique can only tell the frequency
of that violence and not the origins.

Johnson, (1995) suggests that instead of one form of intimate partner violence,
there are in fact two forms - - Common Couple Violence and Patriarchal Terrorism.
Common couple violence he believes is what is being measured by the Conﬂict Tactics
Scale in Straus and Gelles Family Violence Survey (1995). Johnson states that, “some
families suﬁ'er from occasional outbursts of violence ﬁ'om either husbands or wives
(common couple violence) while other families are terrorized by systematic male violence
(patriarch terrorism) (page 282). The types of violence need to be desegregated before

indirect estimation can occur.

2. Measures more severe forms of Violence and Only Physical Violence

The capture-recapture methodology can only measure those cases it captures in
one or more institutional database. Even if there is only a small trace of less severe and
non-physical types of violence, it will capture the rest of those cases in the missing cell.
However, in the case of this study, those institutional databases include authorized cases
from the prosecutor’s ofﬁce, shelter, and counseling. Those cases in the prosecutor’s
database only are included if there is ample evidence of physical abuse for the prosecutor
to take the case assailant to trial. Generally, those cases required hospitalization or other
emergency medical care. Ultimately, it is only those cases with the most evidence,
meaning the most physical damage to the victim, that make it to trial or in the very least

result in the arrest of the perpetrator. Similarly, the shelters only can house those women

116

with the most life threatening situations because of lack of space. Those cases are deemed
more serious when there has been evidence of more extreme injuries. The ﬁles of the
shelter residents contained photos of women with serious injuries such as bruises,
swelling, cuts, and broken bones. Furthermore, the very nature of a “shelter” is an
indicator of the severity of the violence because the residents are there because of their
fear of harm from an intimate assailant.

Studies have revealed that on average the clients of shelters experience 65-68
beatings per year (Johnson, 1995). A necessary assumption of capture-recapture is that at
least some of the cases be captured in the multiple case registries or the technique cannot
estimate the missing cases. Since none of the women in all three of the databases
appeared more than twenty times, we can assume the incidence estimations are
undercounts. Less credence should be placed on the incidence for this reason, however,
the measures of prevalence are adequately represented in a three data systems. Once
capture-recapture establishes a better prevalence rate, a combination of capture-recapture
with survey research could better determine the incidence and resolve this

methodological barrier.

3. Does not provide individual level data

The capture-recapture techniques provides estimates of the population while it
does not provide individual level data. While it is possible to produce estimates for total
counts within categories such as age or racial groups, it is not possible to use the capture-

recapture estimates for analysis of desegregated cases.

117

G. Conclusion

This study was able to provide better estimates and characteristics of victims of
intimate partner violence by using the technique capture-recapture. This dissertation
establishes capture-recapture as a powerful research technique to estimate the size of
populations for empirically testing existing theories and for ﬁrrther theoretical

development.

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